SOLUTION: Find two square roots for the following complex number. Leave your answers in trigonometric form. (Enter your angles in degrees. Do not use cis form.) 4(cos 20° + i sin 20°)

Algebra ->  Vectors -> SOLUTION: Find two square roots for the following complex number. Leave your answers in trigonometric form. (Enter your angles in degrees. Do not use cis form.) 4(cos 20° + i sin 20°)      Log On


   

Question 1080022: Find two square roots for the following complex number. Leave your answers in trigonometric form. (Enter your angles in degrees. Do not use cis form.)
4(cos 20° + i sin 20°)
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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One value of the square root is 2*(cos(10°) + i*sin(10°)).


The other value is 2*(-cos(10°) - i*sin(10°)),  which is the opposite number to the first one.


There is a bunch of lessons on complex numbers
    - Complex numbers and arithmetical operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
    - Raising a complex number to an integer power
    - How to take a root of a complex number (*)
    - Solution of the quadratic equation with real coefficients on complex domain
    - How to take a square root of a complex number (*)
    - Solution of the quadratic equation with complex coefficients on complex domain

    - Solved problems on taking roots of complex numbers (*)
    - Solved problems on arithmetic operations on complex numbers
    - Solved problem on taking square root of complex number (*)
in this site.


From this list, the lessons marked by (*) specially relate to taking roots and square roots of complex numbers.
So, these lessons specially relate to your problem.


Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Complex numbers".