If Z= 2+2i, what is z^4?
Answer:
D. 64 (cos(pi)+isin(pi))
Step-by-step explanation:
Put 2+2i into trigonometric form, raise the r value to the power of 4, and multiply the angle value (theta) by 4 to get the equation of z^4. In this case, r was 2(sqrt2), which raised to the 4th power was 64. The angle value was pi/4, which multiplied by 4 was pi. That's how we get the answer:
64 (cos(pi)+isin(pi)). How this helps!
Following are the calculation to the given value:
Given:
[tex]\to Z= 2+2i[/tex]
To find:
[tex]Z^4=?[/tex]
Solution:
[tex]\to Z= 2+2i[/tex]
[tex]\therefore\\\\i^2= -1[/tex]
[tex](a+b)^2= a^2+b^2+2ab[/tex]
Square the given value:
[tex]\to Z^2= (2+2i)^2[/tex]
[tex]= 2^2+(2i)^2+2 \times 2 \times 2i\\\\= 4+4i^2+8i\\\\= 4-4+8i\\\\=8i[/tex]
When [tex]Z^2= 8i[/tex] then again square the value
[tex]\to ( Z^2)^2= (8i)^2\\\\\to Z^4= 64i^2\\\\\to Z^4= -64\\\\[/tex]
Therefore, the final answer is "-64".
Learn more:
brainly.com/question/25250313
What are the coefficients and constants of 7+5x need fast!!!!
Answer:
35
Step-by-step explanation:
there u go have a great day!
f) Cosec2A + Cot4A = CotA – Cosec4A
Answer:
True (the sides are equal)
I hope this helps!
pls help this is due today!!! if correct I'll make Brainliest!!!!
1= 1/8
2= 4/8
3= 2/8
Step-by-step explanation:
Need help with this
Answer:
The value of x is 25
Step-by-step explanation:
A secant is a line that intersects a circle in exactly two points. When two secants, intersect at a point outside a circle then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcsIn the given figure
→ In circle O
∵ GB and GD intersect it at points F, B, and E, D
∴ GB and GD are secants of circle O
∵ GB and GD intersect outside the circle O at point G
∵ They intercepted arcs EF and BD
→ By using the rule above
∴ m∠G = [tex]\frac{1}{2}[/tex] (m arc BD - m arc EF)
∵ m arc BD = m arc BC + m arc CD
∵ m arc BC = 35° and m arc CD = 100°
∴ m arc BD = 35 + 100 = 135°
∵ m arc EF = x
∵ m∠G = 55°
→ Substitute them in the rule above
∴ 55 = [tex]\frac{1}{2}[/tex] (135 - x)
→ Multiply both sides by 2 to cancel the fraction [tex]\frac{1}{2}[/tex]
∵ 110 = 135 - x
→ Subtract 135 from both sides
∴ -25 = -x
→ Divide both sides by -1
∴ 25 = x
∴ The value of x is 25
When we solve the inequality, will we keep or switch the inequality sign?
−2x>13
Keep
Switch
Answer:
switch I think cuz there is a negative
Step-by-step explanation:
Hope u have a nice day
Answer:
switch
Step-by-step explanation:
whenever u divide a number by a negative number across the inequality, the inequality sign switches
Question 22 of 25
Which of the following are solutions to the quadratic equation below?
Check all that apply.
3x2 - 7x-3 = x
D A. 1
B. 3
] j
C. -3
D. -4
E.
=
1
O F..2
Solve the system of linear equations by substitution.
1/2x +y=-4
y = 2x + 16
Answer:
y = 0
x = -8
Step-by-step explanation:
1/2x + y = - 4
y = 2x + 16
1/2x + (2x + 16) = - 4
1/2x + 2x = - 4 - 16
5/2x = -20
2/5 x 5/2x = -20 x 2/5
x = -40/5
x = -8
y = 2x + 16
y = 2(-8) + 16
y = -16 + 16
y = 0
Check:
1/2x + y = - 4
y = 2x + 16
1/2(-8) + (0) = -4
-4 + 0 = -4
-4 = -4
y = 2x + 16
(0) = 2(-8) + 16
0 = -16 + 16
0 = 0
A statistics teacher announces to the class at the beginning of the semester that there is a 40% chance that a randomly chosen student will finish the semester with an A in the class and there is a 60% that a randomly chosen student will get an A on a test during the semester. Is the probability that a randomly chosen student receives an A in the class and an A on a test during the semester equal to 0.24? Yes, because the chance of getting an A on a test and getting an A in the class are mutually exclusive. Yes, because the chance of getting an A on a test and getting an A in the class are mutually exclusive. No, because the chance of getting an A on a test and getting an A in the class are not independent. No, because the chance of getting an A on a test and getting an A in the class are not independent. Yes, because the chance of getting an A on a test and getting an A in the class are independent. Yes, because the chance of getting an A on a test and getting an A in the class are independent. No, because the chance of getting an A on a test and getting an A in the class are not mutually exclusive.
Answer:
c. No, because the chance of getting an A on a test and getting an A in the class are not independent.
Step-by-step explanation:
brainly?
Help me ASAP pls with this
Answer:-15,20
Step-by-step explanation:
a sandbox is in the shape of a right triangle. The two legs measure 9 inches and 16 inches. what is the perimeter of the sandbox?
Answer:
Perimeter = 50 inches
Step-by-step explanation:
Use pythagoreon theorem to find the hypotenuse
a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9 + 16 + 25 = perimeter
perimeter = 50
A new pair of boots is priced at $123.75, plus 6% sales tax. What is the total cost of the boots?
Answer:
131.18
Step-by-step explanation:
Write 3 9/10 as an improper fraction.
Answer:
39/10
Step-by-step explanation:
Answer:
39/10
Step-by-step explanation:
to make 3 9/10 an improper fraction all you have to do is take the whole number-3 and take the denominator-10 and multiply them 3 x 10 = 30, then add it to the numerator 9 + 30 equals 39 this is your new numerator
The regular price of a CD player is $89. It is on sale at a 25% discount. What is the sale price of the CD player?
Answer:
$66.75
Step-by-step explanation:
You would multiply $89 by .25 to find out what 25% is, then subtract that from $89 to get $66.75
Answer:
$66.75
Step-by-step explanation:
Find the value of x
Answer: x= 108
Step-by-step explanation: The triangle is an isosceles triangle, so the two sides are parallel which means the other angle equals to 72 as well. Now we take the triangle rule and do 180-72-72= 36 (the top angle= 36). The triangles are all equal so that means the other angle (in the upside down one) also equals 72 so we take 36+72= 108. Since it is also a parallelogram, the angles are equal.
-5 ≤ -2; Add 7 to both sides
Help pls
Answer:
2 ≤ 5
Step-by-step explanation:
-5 ≤ -2 add 7 to both sides
-5+7 ≤ -2+7 calculate
2 ≤ 5
Plz answer these 2 I’ll mark brainliest
Answer:
16. C
17. B
sorry if i got it wrong
Answer:
THE ANSWER
A
B
Step-by-step explanation:
MARK BRAINLIEST
Help me little brother with his math please
Answer: less,less greater
Step-by-step explanation:
Answer: #1 : less than 930
Answer: #2 : less than 930
Answer: #3 : greater than 930
Hope this helps older sis!
Divide 2+1/2
A. 2
B. 16
C. 8
D. 4
Answer:
the answer would be 4, the number 2 would double since your dividing it by 0.5
Each of the numbers 0, 2, 4, 6, 8, 10, 12, and 14 is written on a separate sheet of paper and placed into a box. One piece of paper is selected at random. Find the probability that the piece of paper selected contains the number 8 or a number less than 12.
Answer:
For the second, all numbers less than 12, that would be 87.5%
Step-by-step explanation:
There are eight numbers. 100 divided by 8 is 12.5. 12.5 multiplied by 7 is 87.5.
lemma get some help plz
Answer:
-2.6f -16
Step-by-step explanation:
add like terms -
-2.6 + 0.3 = -2.6f
and
-12-4 = -16
There are 96 crayons in a box. Janice takes 9 crayons. How many are left?
Answer:
87
Step-by-step explanation:
Answer:
87 crayons
Step-by-step explanation:
96-9=87
Factorize;Answer the tick one i will mark you as brainlist please quickly step by step explanation also please show it clearly i will mark you as brainlist
Answer:
Solved only ticked ones
4a² + 49b² = (2a + 7b)² - 28ab = 11² - 28*2 = 654x² + 9y² = (2x + 3y)² - 12xy = 12² - 12*6 = 724x² + 9y² = (2x - 3y)² + 12xy = 2² + 12*8 = 10016x² + 25y² = (4x - 5y)² + 40xy = 6² + 40*8 = 356Answer:
use the formula:
[tex]a {}^{2} + {b}^{2} = (a + b) {}^{2} - 2ab[/tex]
1) 4a² + 49b²
= 2²a² + 7²b²
= (2a)² + (7b)²
based on the formula above, a = 2a and b = 7b
= ( 2a + 7b )² - 2(2a)(7b)
substitute 2a+7b = 11 into the equation
= 11² - 2( 14ab )
= 121 - 28ab
substitute ab = 2 into the equation
= 121 - 28(2)
= 121 - 56
= 65
2) 4x² + 9y²
= 2²x² + 3²y²
= (2x)² + (3y)²
based on the formula, a = 2x and b = 3y
= ( 2x + 3y )² - 2(2x)(3y)
substitute 2x+3y = 12 into the equation
= 12² - 2(2x)(3y)
= 144 -2(6xy)
= 144 - 12xy
substitute xy = 6 into the equation
= 144 - 12(6)
= 144 - 72
= 72
3) 4x² + 9y²
= 2²x² + 3²y²
= (2x)² + (3y)²
= (2x)² - (-3y)²
based on the formula, a=2x and b=-3y
= ( 2x-3y )²- 2(2x)(-3y)
substitute 2x-3y = 2 into the equation
= (2)² - 2(2x)(-3y)
= 4 - 2( -6xy )
= 4 + 12xy
substitute xy = 8 into the equation
= 4 + 12(8)
= 4 + 96
= 100
4) 16x² + 25y²
= 4²x² + 5²y²
= (4x)² + (5y)²
= (4x)² - (-5y)²
based on the formula, a = 4x and b = -5y
= (4x-5y)² - 2(4x)(-5y)
substitute 4x-5y = 6
= (6)² -2(4x)(-5y)
= 36 -2(-20xy)
= 36 + 40xy
substitute xy = 8 into the equation
= 36 + 40(8)
= 36 + 320
= 356
ahhhh I need help please!!
Answer:
two teaspoons i think sorry if this doesnt help
Step-by-step explanation:
Collin is playing a video game. He wins 25 points for each gold coin he finds. His goal is to win more than 200 points. He wants to know how many gold coins he needs to find.
Answer:
200/25×1
=8 gold coins
Step-by-step explanation:
The required number of gold coins he needs is given 8 coins.
Given that,
Collin is playing a video game. He wins 25 points for each gold coin he finds. His goal is to win more than 200 points.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
1 coin = 25 points
For 200 points number of coins is given as = 200 / 25 = 8 coins
Thus, the required number of gold coins he needs is given 8 coins.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
What is the common factors of 9 and 67
Please don't google it
Answer:
1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
9 1, 3 9
67 1 and 67
so just enjoy ur day and have a great Christmas and new year
can someone help me with the equation(s)
She purchased 8 sports drinks
{d=p+3
2.25p+1.25d=21.25
d=p+3
p=d - 3
2.25(d - 3) + 1.25d = 21.25
2.25(d-3) + 1.25d=21.25
2.25 - 6.75 + 1.25d = 21.25
3.5d = 21.25+6.75
d=28/3.5
D=8
17/6 + 4/3 fractions
Answer:
25/6
Step-by-step explanation:
I multiplied 4/3 by 2, so the new fraction is 8/6. You add 17/6 with 8/6, and you get 25/6. I hope you understand.
Bianca set the thermostat in her house to 87°F, which was 13° warmer than the temperature outside. What temperature was it outside?
Confused.
Answer: 74 degrees Fahrenheit
Step-by-step explanation: the temperature outside was 13 degrees lower than 87 degrees, so 87 - 13 = 74
Answer:
74 degrees F
Step-by-step explanation:
Subtract the 87 - 13
This is because there are +13 degrees more than outside. So if you add 74 + 13 that were added by the thermostat, you get 87 degrees. Does it make sense?
Just subtract :)
Answer!
A car travels from A to B at a speed of 30 mph then returns, using the same road, from B to A at a speed of 65 mph. What is the average speed for the round trip?
Answer:
41 mphStep-by-step explanation:
s₁ = s₂ = x {the distance from A to B}
s = s₁ + s₂ = x + x = 2x {the distance of the round trip}
t = t₁ + t₂ {the time of the round trip}
v₁ = 30 mph
v₂ = 65 mph
t₁ = s₁/v₁ = x/30 h {the time of trip from A to B}
t₂ = s₂/v₂ = x/65 h {the time of trip from B to A}
The average speed:
[tex]v=\dfrac st=\dfrac{2x}{\frac x{30}+\frac x {65}}=\dfrac{2x}{x(\frac 1{30}+\frac1 {65})}=\dfrac{2}{\frac{13}{390}+\frac6{390}}=2\cdot\frac{390}{19}=41.05263...\approx41[/tex]