Question

help plz.
Express each complex number in polar form.
(a) 4 + 3i
b) -5 – 2i

Answer 1

HI!!

Answer 2

you need two numbers to write
\[4+3i\] as \[r(\cos(\theta)+i\sin(\theta)\] namely \(r\) and \(\theta\)

Answer 3

\(r\) is easiest, it is the absolute value or \(\sqrt{a^2+b^2}\)

Answer 4

then for \(\theta\) depending on what quadrant you are in, it may be
\[\theta=\tan^{-1}(\frac{b}{a})\]

Answer 5

that will work for \(4+3i\) it will not work for \(-5-2i\)because you are in quadrant 3 there