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, $r(\cos \theta + i\sin \theta)$, where $r = 2$, $\theta = 230^\circ$. To convert it to standard form, calculate $a = r\cos\theta$ and $b = r\sin\theta$. Using a calculator, $a = 2\cos(230^\circ) \approx -1.29$ and $b = 2\sin(230^\circ) \approx -1.53$. Therefore, the standard form is $-1.29 - 1.53i$.

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 $2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$