Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-$\left( 12 \operatorname { cis } 13.5 ^ { \circ } \right) \left( 2 \operatorname { cis } 7.5 ^ { \circ } \right)$
A) $22.4059 + 8.6008 \mathrm { i }$
B) $- 6.5728 + 10.0399 \mathrm { i }$
C)
$- 1.0955 \mathrm { i }$
D)
$+ 22.4059 \mathrm { i }$

Question

Quizplus · Accepted Answer

When multiplying two complex numbers in polar form, you multiply their magnitudes and add their angles. Here, $12 \operatorname{cis} 13.5^\circ$ and $2 \operatorname{cis} 7.5^\circ$ are multiplied, resulting in a magnitude of $12 \times 2 = 24$ and an angle of $13.5^\circ + 7.5^\circ = 21^\circ$. Converting back to rectangular form using $x = r \cos(\theta)$ and $y = r \sin(\theta)$ with $r = 24$ and $\theta = 21^\circ$, we get the correct answer in rectangular form, which matches option A.

Perform the Indicated Operation (12cis⁡13.5∘)(2cis⁡7.5∘)\left( 12 \operatorname { cis } 13.5 ^ { \circ } \right) \left( 2 \operatorname { cis } 7.5 ^ { \circ } \right)(12cis13.5∘)(2cis7.5∘)

Perform the Indicated Operation $\left( 12 \operatorname { cis } 13.5 ^ { \circ } \right) \left( 2 \operatorname { cis } 7.5 ^ { \circ } \right)$