Question

Write the complex number in polar form with argument θ between 0 and 2π.
7+7(sqrt)3i

Answer 1

\[7+7\sqrt{3}i\] in polar form
you need two numbers, \(r=\sqrt{a^2+b^2}\) and \(\theta\)
in this example you can use \(\theta=\tan^{-1}(\frac{b}{a})\) because you are in quadrant 1

Answer 2

theta you can just about do in your head, it is \(\frac{\pi}{3}\) but if it is not clear we can get that second
\(r\) is routine, it is \(\sqrt{7^2+7\sqrt{3})^2}=\sqrt{49+3\times 7^2}=\sqrt{4\times 7^2}=14\)

Answer 3

that was king of show offy, you can also just compute
\[\sqrt{7^2+(7\sqrt{3})^2}=\sqrt{49+147}=\sqrt{196}=14\]

Answer 4

and \(\theta=\tan^{-1}(\frac{\sqrt{3}}{2})=\frac{\pi}{3}\)

Answer 5

you got this?

Answer 6

AHHH thank you sooo much!! I really appreciate it!

Answer 7

I just got caught up on the algebra in the square root. THANK YOU!!

Answer 8

yw