Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.
$( - 4 - 4 i ) ( - 3 - 3 i )$

A) $- 12 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

B) $- 24 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$

C) $12 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

D) $24 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

E) $12 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$

Question

Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.
$( - 4 - 4 i ) ( - 3 - 3 i )$

A) $- 12 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

B) $- 24 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$

C) $12 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

D) $24 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

E) $12 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$

Quizplus · Accepted Answer

The product of two complex numbers in trigonometric form is found by multiplying their magnitudes and adding their angles. For $(-4 - 4i)$ and $(-3 - 3i)$, their magnitudes are $4\sqrt{2}$ and $3\sqrt{2}$ respectively, and both have an angle of $\frac{5\pi}{4}$ (225 degrees, in the third quadrant). Multiplying the magnitudes gives $24$, and adding the angles gives $\frac{5\pi}{2}$, which simplifies to $\frac{\pi}{2}$ due to periodicity. Thus, the product is $24(\cos(\frac{\pi}{2}) + i\sin(\frac{\pi}{2}))$.

Perform the Indicated Operation Using Trigonometric Form (−4−4i)(−3−3i)( - 4 - 4 i ) ( - 3 - 3 i )(−4−4i)(−3−3i)

Perform the Indicated Operation Using Trigonometric Form $( - 4 - 4 i ) ( - 3 - 3 i )$