Write the complex number in rectangular form.
-$4 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)$
A) $3.9 + 1 \mathrm { i }$
B) $1.9 + 0.5 \mathrm { i }$
C) $- 1.9 - 0.5 \mathrm { i }$
D) $1 + 3.9 \mathrm { i }$

Question

Quizplus · Accepted Answer

The given complex number is in polar form. To convert it to rectangular form, use the formula $x = r\cos(\theta)$ and $y = r\sin(\theta)$, where $r = 4$ and $\theta = 15^\circ$. Thus, $x = 4\cos(15^\circ)$ and $y = 4\sin(15^\circ)$. Calculating these values gives a complex number close to $3.9 + 1i$, which matches choice A.

Write the Complex Number in Rectangular Form 4(cos⁡15∘+isin⁡15∘)4 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)4(cos15∘+isin15∘)

Write the Complex Number in Rectangular Form $4 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)$