Question C.6: Complex Operations Assume Z1 = 3∠45°, Z2 = 4∠45°, calculate ...
Complex Operations
Assume Z_1=3 \angle 45^{\circ}, Z_2=4 \angle 45^{\circ}, calculate Z_1+Z_2, Z_1 Z_2, and Z_1 / Z_2.
First, convert Z_1 and Z_2 to rectangular form, then add them.
Using Equation (B.1):
L(x(t))=X(s)=\int_0^{\infty} x(t) e^{-s t} dt (B.1)
The real part a of the Z_1 is:
a=3 \times \cos \left(45^{\circ}\right)=2.1213The imaginary part b of the Z_1 is:
b=3 \times \sin \left(45^{\circ}\right)=2.1213The real part c of the Z_2 is:
c=4 \times \cos \left(45^{\circ}\right)=2.8284The imaginary part d of the Z_2 is:
d=4 \times \sin \left(45^{\circ}\right)=2.8284Therefore:
Z_1+Z_2=2.1213+j 2.1213+2.8284+j 2.8284=4.9497+j 4.9497Convert the result to polar form:
\begin{aligned}Z_1+Z_2 &=7 \angle 45^{\circ} \\Z_1 \times Z_2 &=(3 \times 4) \angle\left(45^{\circ}+45^{\circ}\right)=12 \angle 90^{\circ} \\\frac{Z_1}{Z_2} &=\frac{3}{4} \angle\left(45^{\circ}-45^{\circ}\right)=0.75 \angle 0^{\circ}\end{aligned}Related Answered Questions
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