Question

Write the complex number in polar form with argument θ between 0 and 2π.
−2 + 2i

Answer 1

for \(c=a+bi \ \in \mathbb{C} \) radius is given by \(r = \sqrt{a^2+b^2}\)
we know that your point lies in the 2nd quadrant in the complex plane so
\(\theta=\arctan(\frac{2}{-2})+\pi=\arctan(-1)+\pi\)

in general
if the point is in the 1st or 3rd quadrant
we have
\(a+bi\iff(r,\theta)=(\sqrt{a^2+b^2},\arctan(\frac{b}{a}))\)
else
\[a+bi\iff(r,\theta)=(\sqrt{a^2+b^2},\arctan(\frac{b}{a})+\pi))\]

Answer 2

that should say if the point is in the 1st or \(\color{red}{4th}\) quadrant

Answer 3

thank you

Answer 4

no problem