Answer
Step 1. See figure.
Step 2. $5cos(\frac{3\pi}{2})+5i\ sin(\frac{3\pi}{2})$
Work Step by Step
Step 1. Given the complex number $-5i$, we can identify $a=0, b=-5$ as $(0,-5)$ in complex coordinates as shown in the figure.
Step 2. Using the above results, we can get the modulus as $r=\sqrt {a^2+b^2}=\sqrt {(0)^2+(-5)^2}=5$. The polar angle can be found as $\theta=\frac{3\pi}{2} $ (on negative y-axis).
Thus, we can write the complex number in polar form as $-5i=5cos(\frac{3\pi}{2})+5i\ sin(\frac{3\pi}{2})$
