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thereddevils
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Homework Statement
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|
Homework Equations
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?