What is the polar form of $- 2 + 9 i$ $-2 + 9i$ ?

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Answer 1 · 2018-06-25T10:27:08

Polar form is given by $ρ_{θ}$ $rho_theta$ where $ρ = | z |$ $rho=absz$ and $θ$ $theta$ is the angle formed by complex number and x-axis

First we draw the complex number in coordinate axis system and notice that the angle is bigger than 90 degrees

$| z | = \sqrt{4 + 81} = \sqrt{85}$ $absz=sqrt(4+81)=sqrt85$

And $tan α = \frac{2}{9}$ $tanalpha=2/9$ where $α$ $alpha$ is angle formed by complex and y-axis, then we will add this angle to 90 degrees

$alpha=12º 31´$ and $theta=alpha+90=102º 31´$

The number in polar form is $sqrt85_(102º,31´)$

What is the polar form of -2 + 9i−2+9i-2 + 9i?