1. The problem statement, all variables and given/known data Given that arg(z/(1-i))=pi/2, find the argument of z. Sketch , in the Argand diagram , the set of points representing z and the point representing the complex number w=-4+3i. Hence deduce the least value of |z+4-3i| 2. Relevant equations 3. The attempt at a solution Let z=a+bi Rationalising z/(1-i)=(a-b)/2+(a+b)/2 i negative pi/2 suggest that the point is on the negative y-axis. tan pi/2 = [(a-b)/2]/[(a+b)/2] hence a=b And since (a+b)/2 is negative, a<0 , b<0 so z=a+ai or b+bi (a,a) is in the third quadrant, and the argument of z is -3pi/4 I have no problem in sketching. The problem i have is with the last part. Any pointers?