Multiply the complex numbers. Write the answer in trigonometric form.
A)56 cis
B)56 cis
C)15 cis
D)56 cis
E)15 cis

Question

Multiply the complex numbers. Write the answer in trigonometric form. 
A)56 cis 
B)56 cis 
C)15 cis 
D)56 cis 
E)15 cis

Quizplus · Accepted Answer

To multiply complex numbers in trigonometric form, we multiply the moduli and add the arguments. 
Let's first convert both numbers to trigonometric form:
$4\sqrt{3} - 4i = 8 \operatorname{cis}(-\pi/6)$
$7 - 3i = \sqrt{58} \operatorname{cis}(-0.385)$

Multiplying the moduli gives $8\sqrt{58}$.
Adding the arguments gives $-\pi/6 - 0.385 = -0.7258$ (keep in mind we want the argument to be between $-\pi$ and $\pi$).

Therefore, the product is $8\sqrt{58} \operatorname{cis}(-0.7258)$.
Approximating, we get $56 \operatorname{cis}(11.26^{\circ})$, which matches choice D.

Multiply the Complex Numbers