SOLUTION: Hello Tutor, I really need your help to answer this question. How are polar coordinates useful for working with complex numbers (hint: think about powers and roots)?

Question 972923: Hello Tutor, I really need your help to answer this question.
How are polar coordinates useful for working with complex numbers (hint: think about powers and roots)?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Check DeMoivre's Theorem and the Argand diagram.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Calculating the nth power or the nth root of a complex number in the rectangular form is a complicated, messy business.
Calculate powers and roots of complex numbers in polar form is simple:
For a power: and
for an nth root:

Transforming between polar and rectangular coordinates is also simple,
so if you are given the rectangular form and need to calculate a power or root,
you can easily transform to polar form, and then calculate the desired power or root in polar form.
If the result must be expressed in rectangular form, you just transform your polar form result to rectangular form.

If you have a complex number , or (whichever letter you use for ),
with real part , and imaginary part ,
you can calculate the argument, and modulus from
and .
If you know the argument, and modulus of a complex number,
you can calculate its real part , and imaginary part as
and
RELATED QUESTIONS
Hello Tutor Can you please help me answer this question. How are polar coordinates... (answered by solver91311)
How are polar coordinates useful for working with complex numbers (hint: think about... (answered by math_helper)
Hello Tutor, I really need your help to answer this question please. What are the... (answered by Boreal)
Hello Tutor, I really need your help to answer this question please. What are the... (answered by Edwin McCravy)
Hello Tutor, I really need your help to answer this question please. 2. Solve for x: (answered by Edwin McCravy)
Hello Tutor, I really need your help to answer this question please. 1. If the... (answered by anand429)
Hello! I don't have my notes with me so I'm having difficulty remembering how to solve... (answered by Alan3354)
Hello tutor, I really need your help solving this question please. Solve the system:... (answered by Fombitz)
Hello Tutor, I really need your help solving this question please. Solve the system: y (answered by Boreal,fcabanski)