Question

Find the module and the principal argument of W, z, wz and w/z, given that
(a) w=10i, z=1+i√3
(b) w= -2√3 +2i, z=1-i

Answer 1

(a) $|W|=10,argW=\pi/2, |Z|=\sqrt{1+3}=2, argZ=\pi/3$

$|WZ|=|W||Z|=20, arg(WZ)=argW+argZ=5\pi/6$

$|W/Z|=|W|/|Z|=5, arg(W/Z)=argW-argZ=\pi/6$

(b) $|W|=\sqrt{12+4}=4, argW=5\pi/6, |Z|=\sqrt{1+1}=\sqrt2$

$argZ=7\pi/4$

$|WZ|=4\sqrt2, arg(WZ)=argW+argZ=7\pi/12$

$|W/Z|=4/\sqrt2, arg(W/Z)=argW-argZ=5\pi/6$