Question

Given complex number z=3+4i

Write z in polar form
&
Write z^5 in polar form

Answer 1

you want
\[r\left(\cos(\theta)+i\sin(\theta)\right)\] or
\[re^{i\theta}\]?

Answer 2

r(cos(theta)+isin(theta)) please

Answer 3

how far is the point (3,4) from the origin? and what angle does it make with the positive x axis?

Answer 4

\[r=\sqrt{a^2+b^2}\]

Answer 5

r=5

Answer 6

and that arctangent of 4/3 is?

Answer 7

53.1. so z=5(cos53+isin53) and z^5=3125(cos265+isin265)

Answer 8

seems reasonable enough to me :)