Question

What is the product of 65(cos(14°) + i sin(14°)) and 8(cos(4°) + i sin(4°))?

a) 73(cos(18°) + i sin(18°))
b) 73(cos(56°) + i sin(56°))
c) 520(cos(18°) + i sin(18°))
d) 520(cos(56°) + i sin(56°))

Answer 1

c

Explanation:

edge 2020

Answer 2

`c)\ 520(\cos(18^\circ)+\mathbf{i}\sin(18^\circ)`

Explanation:

Complex Numbers in Polar Form

Let Z1 and Z2 two complex numbers in the form:

`Z1 = r_1(\cos\theta_1+\mathbf{i}\sin\theta_1)`

`Z2 = r_2(\cos\theta_2+\mathbf{i}\sin\theta_2)`

The product of Z1*Z2 is given by:

`Z1*Z2 = r_1*r_2(\cos(\theta_1+\theta_2)+\mathbf{i}\sin(\theta_1+\theta_2))`

The given complex number has:

`r_1=65`

`\theta_1=14^\circ`

`r_1=8`

`\theta_1=4^\circ`

Thus:

`Z1*Z2 = 65*8(\cos(14^\circ+4^\circ)+\mathbf{i}\sin(14^\circ+4^\circ)`

`\mathbf{Z1*Z2 = 520(\cos(18^\circ)+\mathbf{i}\sin(18^\circ)}`