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

Using the formula for multiplying complex numbers in trigonometric form, $(\cos x + i\sin x)(\cos y + i\sin y) = \cos(x+y) + i\sin(x+y)$, the result is $\cos(7^\circ + 24^\circ) + i\sin(7^\circ + 24^\circ) = \cos 31^\circ + i\sin 31^\circ$.

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 $\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)$