Find the standard form of the complex number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$ .
A)8 $$\sqrt { 3 }$$ - 8i
B)-4 $\sqrt { 3 }$ + 4i
C)4 $$\sqrt { 3 }$$ - 4i
D)-8 $\sqrt { 3 }$ + 8i
E)4 + 4 $\sqrt { 3 }$ i

Question

Find the standard form of the complex number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$ . ​
A)​8 $$\sqrt { 3 }$$ - 8i
B)​-4 $\sqrt { 3 }$ + 4i
C)​4 $$\sqrt { 3 }$$ - 4i
D)​-8 $\sqrt { 3 }$ + 8i
E)​4 + 4 $\sqrt { 3 }$ i

Quizplus · Accepted Answer

The standard form of a complex number is $a + bi$, where $a$ and $b$ are real numbers. The given complex number is in polar form, $r(\cos \theta + i\sin \theta)$, where $r = 8$, $\theta = 330^\circ$. The cosine and sine of $330^\circ$ are $\cos 330^\circ = \sqrt{3}/2$ and $\sin 330^\circ = -1/2$, respectively. Thus, the complex number in standard form is $8(\sqrt{3}/2) + 8(-1/2)i = 4\sqrt{3} - 4i$.

Find the Standard Form of the Complex Number 8(cos⁡330∘)+isin⁡330∘8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }8(cos330∘)+isin330∘

Find the Standard Form of the Complex Number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$