Convert a Complex Number from Polar to Rectangular Form
-$10.14 \left( \cos 133.3 ^ { \circ } + i \sin 133.3 ^ { \circ } \right)$
A) $- 7 + 7.4 \mathrm { i }$
B) $7.4 - 7 \mathrm { i }$
C) $- 2.2 + 2.3 \mathrm { i }$
D) $2.2 - 2.3 \mathrm { i }$

Question

Quizplus · Accepted Answer

To convert a complex number from polar to rectangular form, use the formula $x = r \cos \theta$ and $y = r \sin \theta$, where $r$ is the magnitude and $\theta$ is the angle. For $10.14(\cos 133.3^\circ + i\sin 133.3^\circ)$, $x = 10.14 \cos 133.3^\circ \approx -7$ and $y = 10.14 \sin 133.3^\circ \approx 7.4$, making the rectangular form $-7 + 7.4i$.

Convert a Complex Number from Polar to Rectangular Form - 10.14(cos⁡133.3∘+isin⁡133.3∘)10.14 \left( \cos 133.3 ^ { \circ } + i \sin 133.3 ^ { \circ } \right)10.14(cos133.3∘+isin133.3∘)

Convert a Complex Number from Polar to Rectangular Form
- $10.14 \left( \cos 133.3 ^ { \circ } + i \sin 133.3 ^ { \circ } \right)$