Question

How do you calculate square roots of complex numbers? For example sqrt(-16-30i)

Answer 1

You want to square root -16-30i?

Answer 2

right

Answer 3

I checked on wolfram alpha and it told me the answer is 3-5i, but I don't know how to work it out.

Answer 4

3-5i?

Answer 5

yes

Answer 6

can u convert -16-30i into polar form?

Answer 7

x+iy = -16-30i<--cartesian form
r,theta<--polar form
can u convert cartesian to polar form ?

Answer 8

working on it

Answer 9

-16-30i=(34,4.22)

Answer 10

what is 4.22? in radians?

Answer 11

yes

Answer 12

ok, now to get square root of complex number, take square root of magnitude and divide the angle by 2

Answer 13

that is here, take square root of 34

Answer 14

ok, thanks

Answer 15

so did u get 3-5i finally ?

Answer 16

What is the reason for dividing the angle by 2? Must be a trig identity, right?

Answer 17

I did! Thanks for your help.