Question

Given z1 = -3
$\sqrt{3}$
 + 3i and z2 = 6cos150° + 6isin150°, use complete sentences to explain why z1 = z2. Explain the steps of your work for full credit.


​

Answer 1

Answer:

See explanation

Step-by-step explanation:

The given complex number are:

$z_1=-3\sqrt{3}+3i$

and

$z_2=6\cos 150\degree+6i\sin 150\degree$

When we rewrite $z_1=-3\sqrt{3}+3i$ in complex form, we obtain;

$z_1=r(\cos \theta+i\sin \theta)$

where

$r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6$

and

$\theta=tan^{-1}(\frac{y}{x})$

$\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree$

Hence,

$z_1=6(\cos 150\degree+i\sin 150\degree)$

$z_1=6\cos 150\degree+6i\sin 150\degree$

Hence

$z_1=z_2$