Question

Find the root:

Answer 1

\[\sqrt{9-9i}\]

Answer 2

solve z^2 = 9-9i

Answer 3

@jayzdd How do you mean?

Answer 4

you can use the trig form of the complex number
z^2 = sqrt(9^2 + 9^2) ( cos(-45) + i sin(-45) )

Answer 5

you must be knowing that angles add up when you multiply two complex numbers

Answer 6

\[(r_1\angle \theta_1 )(r_2\angle \theta_2) = r_1r_2 \angle (\theta_1+\theta_2)\]

Answer 7

Finding \(\sqrt{9-9i}\) is same as finding a number which when multiplied by itself gives you \(9-9i\)

Answer 8

that is, finding some \(z\) such that
\[z*z = 9-9i\]