Question

use a scientific calculator or unit circle to convert the polar form of the complex number to its equivalent rectangular form.

$z = 32left(cos\frac{pi}{3}+isin\frac{pi}{3}
ight)$

$z=\frac{5sqrt{3}}{2}-\frac{5}{2}i$

$z = 16 + 16isqrt{3}$

$z=-\frac{5sqrt{3}}{2}+\frac{-5}{2}i$

$z=-16 - 16isqrt{3}$

Explanation:

Step1: Record valores trigonométricos

Conocemos que $\cos\frac{\pi}{3}=\frac{1}{2}$ y $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$.

Step2: Expandir la forma polar

Dado $z = 32(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3})$, sustituimos los valores trigonométricos: $z = 32(\frac{1}{2}+i\frac{\sqrt{3}}{2})$.

Step3: Realizar la multiplicación

$z=32\times\frac{1}{2}+32\times i\frac{\sqrt{3}}{2}=16 + 16i\sqrt{3}$.

Answer:

$z = 16+16i\sqrt{3}$