# Moivre 2

Find the cube roots of 125(cos 288° + i sin 288°).

Result

r =  5
α1 =  96 °
α2 =  216 °
α3 =  336 °

#### Solution:

$r=\sqrt[3]{ 125 } = 5$
$\alpha _1=288/3+0 \cdot \ 360/3 = 96 ^\circ$
$\alpha _2=288/3+1 \cdot \ 360/3 = 216 ^\circ$
$\alpha _3 = 288/3+2\cdot 360/3 = 336 ^\circ \ \\ z_1 = 5 ( \cos 96 + i \sin 96 ) \ \\ z_2 = 5 ( \cos 216 ^\circ + i \sin 216 ^\circ ) \ \\ z_3 = 5 ( \cos 336 ^\circ + i \sin 336 ^\circ )$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Try our complex numbers calculator.
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. De Moivre's formula
There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers.
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
3. Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
5. Linear imaginary equation
Given that ? "this is z star" Find the value of the complex number z.
6. Reference angle
Find the reference angle of each angle:
7. Calculation
How much is sum of square root of six and the square root of 225?
8. Goniometric form
Determine goniometric form of a complex number ?.
9. Log
Calculate value of expression log |3 +7i +5i2| .
10. Reciprocal
Calculate reciprocal of z=0.8-1.8i:
11. Im>0?
Is -10i a positive number?
12. ABS CN
Calculate the absolute value of complex number -15-29i.
13. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
14. Complex number coordinates
Which coordinates show the location of -2+3i
15. Is complex
Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
16. Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
17. Angles 1
It is true neighboring angles have not common arm?