Answer:
[tex]c)\ 520(\cos(18^\circ)+\mathbf{i}\sin(18^\circ)[/tex]
Step-by-step explanation:
Complex Numbers in Polar Form
Let Z1 and Z2 two complex numbers in the form:
[tex]Z1 = r_1(\cos\theta_1+\mathbf{i}\sin\theta_1)[/tex]
[tex]Z2 = r_2(\cos\theta_2+\mathbf{i}\sin\theta_2)[/tex]
The product of Z1*Z2 is given by:
[tex]Z1*Z2 = r_1*r_2(\cos(\theta_1+\theta_2)+\mathbf{i}\sin(\theta_1+\theta_2))[/tex]
The given complex number has:
[tex]r_1=65[/tex]
[tex]\theta_1=14^\circ[/tex]
[tex]r_1=8[/tex]
[tex]\theta_1=4^\circ[/tex]
Thus:
[tex]Z1*Z2 = 65*8(\cos(14^\circ+4^\circ)+\mathbf{i}\sin(14^\circ+4^\circ)[/tex]
[tex]\mathbf{Z1*Z2 = 520(\cos(18^\circ)+\mathbf{i}\sin(18^\circ)}[/tex]
