calculate n plot (uv)18 if u is 2-2i and v 1-1i

Question

calculate n plot (uv)18 if u is 2-2i and v 1-1i

Answer 1

First method to determine answer is to use FOIL method -

18 u v = 18 (2-2i) (1-1i) = 18 (2-2i-2i-2) = 18 (-4i) = -72i, this means magnitude of 72 units along the i - axis pointed down from the orgin.

Second method to do this involves multiplying phasors (multiply magnitudes and add angles).

u = (2-2i) = 2SQRT(2) @ 315 deg

v = (1-1i) = SQRT(2) @ 315 deg

18 u v = 18 * 2 * SQRT(2)^2 @ 630 deg = 72 @ 270 deg. this means 72 units along the i - axis pointed down from the origin.

hope this helps!