Find the standard form of the complex number shown below.Round answers to two decimal places. $2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$
A) -1.29 - 1.53i
B) -2.53 - 2.88i
C) -2.04 - 2.63i
D) -1.52 - 1.92i
E) -2.71 - 3.06i

Question

Find the standard form of the complex number shown below.Round answers to two decimal places.   $2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$
A) -1.29 - 1.53i
B) -2.53 - 2.88i
C) -2.04 - 2.63i
D) -1.52 - 1.92i
E) -2.71 - 3.06i

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 and can be converted to standard form using the formula $r(\cos \theta + i\sin \theta)$, where $r = 2$, $\theta = 230^\circ$. Calculating $a = r\cos \theta = 2\cos 230^\circ \approx -1.29$ and $b = r\sin \theta = 2\sin 230^\circ \approx -1.53$, we get the standard form as $-1.29 - 1.53i$.

Find the Standard Form of the Complex Number Shown Below 2(cos⁡230∘+isin⁡230∘)2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)2(cos230∘+isin230∘)

Find the Standard Form of the Complex Number Shown Below $2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$