Find the product. Write the product in rectangular form, using exact values.
-$\left[ 7 \left( \cos 120 ^ { \circ } + \mathrm { i } \sin 120 ^ { \circ } \right) \right] \left[ 2 \left( \cos 90 ^ { \circ } + \mathrm { i } \sin 90 ^ { \circ } \right) \right]$
A) $- 7 \sqrt { 3 } - 7 \mathrm { i }$
B) $5 \sqrt { 6 } - \sqrt { 2 } \mathrm { i }$
C) $7 \sqrt { 3 } - 28 \mathrm { i }$
D) $14 - 14 \sqrt { 3 } \mathrm { i }$

Question

Quizplus · Accepted Answer

The product of two complex numbers in rectangular form is found by multiplying the real parts, the imaginary parts, and the two imaginary units.$\left[ 7 \left( \cos 120 ^ { \circ } + \mathrm { i } \sin 120 ^ { \circ } \right) \right] \left[ 2 \left( \cos 90 ^ { \circ } + \mathrm { i } \sin 90 ^ { \circ } \right) \right]$$\left[ 7 \left( -\frac{1}{2} + \mathrm { i } \frac{\sqrt{3}}{2} \right) \right] \left[ 2 \left( 0 + \mathrm { i } 1 \right) \right]$$\left[ -\frac{7}{2} + \mathrm { i } \frac{7\sqrt{3}}{2} \right] \left[ 0 + \mathrm { i } 2 \right]$$\left[ -\frac{7}{2} \cdot 0 + \mathrm { i } \frac{7\sqrt{3}}{2} \cdot 0 + \mathrm { i } -\frac{7}{2} \cdot 2 + \mathrm { i }^2 \frac{7\sqrt{3}}{2} \cdot 2 \right]$$\left[ 0 + 0 - 7 \mathrm { i } + (-1) \cdot \frac{7\sqrt{3}}{2} \cdot 2 \right]$$\left[ - 7 \mathrm { i } - 7\sqrt{3} \right]$

Find the Product A) −73−7i- 7 \sqrt { 3 } - 7 \mathrm { i }−73​−7i

Find the Product A) $- 7 \sqrt { 3 } - 7 \mathrm { i }$