Find the standard form of the complex number shown below. Round answers to two decimal places.
$$6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$$
A) $- 5.91 - 1.04 i$
B) $- 6.14 - 1.43 i$
C) $- 6.66 - 2.14 i$
D) $- 7.15 - 2.39 i$
E) $- 7.33 - 2.57 i$

Question

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 $r = 6$, $\theta = 190^\circ$. To convert it to standard form, calculate $a = r\cos\theta = 6\cos190^\circ$ and $b = r\sin\theta = 6\sin190^\circ$. Using a calculator, $a \approx -5.91$ and $b \approx -1.04$, so the standard form is $-5.91 - 1.04i$.

Find the Standard Form of the Complex Number Shown Below 6(cos⁡190∘+isin⁡190∘)6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)6(cos190∘+isin190∘)

Find the Standard Form of the Complex Number Shown Below $6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$