This is a free lesson from our course in Trigonometry
In this lesson you'll learn with the help of some examples and practice questions
with solution, how to find roots of complex numbers. For complex number z = r
(cos
+ i sin
), then for a positive
integer n, n^{th} root is given by ^{n}r[cos
{(+ 2k)/n}
+ i sin {(+ 2k)/n}]
for values of k from 0, 1, 2, ......, n  1. For example, if you are asked to find fourth roots of the
complex number z = 5(cos
/3 + i sin
/3), all you need to
do is to plug values into the formula. Here, n = 4, r = 5,
=
/3. Since n is 4, use
the values of k = 0, 1, 2, 3.
(More text below video...)
(Continued from above) The roots are: ^{4}5(cos
/12 + i sin
/12) ^{4}5(cos
7/12 + i sin 7/12) ^{4}5(cos
13/12 + i sin 13/12) ^{4}5(cos
19/12 + i sin 19/12)
Similarly, to find cube roots of 1, first you write it in the polar form and then
plug the values in formula three times. The roots are (1/2) + (3/2)i,
1, and (1/2)  (3/2)i.
Once you go through the explanation by instructor in the video, it'll be easy for
you to understand how the roots of complex numbers determined.
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