Perform the operation and leave the result in trigonometric form. $$\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)$$
A)cos 17° - isin 17°
B)cos 31° - isin 31°
C)cos 17° + isin 17°
D)cos 31° + icos 31°
E)cos 31° + isin 31°

Question

Perform the operation and leave the result in trigonometric form.​ $$\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)$$ ​
A)cos 17° - isin 17°
B)cos 31° - isin 31°
C)cos 17° + isin 17°
D)cos 31° + icos 31°
E)cos 31° + isin 31°

Quizplus · Accepted Answer

The product of two complex numbers in trigonometric form, $\left( \cos \alpha + i \sin \alpha \right)$ and $\left( \cos \beta + i \sin \beta \right)$, is given by $\left( \cos (\alpha + \beta) + i \sin (\alpha + \beta) \right)$. Therefore, the product of $\left( \cos 7^\circ + i \sin 7^\circ \right)$ and $\left( \cos 24^\circ + i \sin 24^\circ \right)$ is $\left( \cos (7^\circ + 24^\circ) + i \sin (7^\circ + 24^\circ) \right) = \cos 31^\circ + i \sin 31^\circ$.

Perform the Operation and Leave the Result in Trigonometric Form (cos⁡7∘+isin⁡7∘)(cos⁡24∘+isin⁡24∘)\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)(cos7∘+isin7∘)(cos24∘+isin24∘)

Perform the Operation and Leave the Result in Trigonometric Form $\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)$