Find input impedance at 30 degrees from the load?

Question

load impedance=20+j31-ohms

Answer 1

1) find the angle of the load impedance:
angle = tan^-1(31/20) = 57.17 degrees

2) add 30 degrees to that: 87.17

3) find the magnitude of the load impedance:
mag^2 = 20^2 + 31^2
mag = 36.89

4) find the new cartesian coordinates for 36.89 /_ 87.17
1.82 + j36.84

note: this is almost a purely capacitive impedance.

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