Find the standard form of the complex number shown below. Round answers to two decimal places.
$$2 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$$
A) $1.88 - 0.68 i$
B) $2.11 - 1.07 i$
C) $2.63 - 1.78 i$
D) $3.12 - 2.03 i$
E) $3.30 - 2.21 i$

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 $r = 2$, $\theta = 340^\circ$. To convert it to standard form, calculate $a = r\cos\theta = 2\cos340^\circ$ and $b = r\sin\theta = 2\sin340^\circ$. Using a calculator, $\cos340^\circ \approx 0.94$ and $\sin340^\circ \approx -0.34$, so $a \approx 2 \times 0.94 = 1.88$ and $b \approx 2 \times -0.34 = -0.68$. Therefore, the standard form is $1.88 - 0.68i$.

Find the Standard Form of the Complex Number Shown Below 2(cos⁡340∘+isin⁡340∘)2 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)2(cos340∘+isin340∘)

Find the Standard Form of the Complex Number Shown Below $2 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$