Question

If the amplitude of z-2-3i is π/4, then the locus of z=x+iy is:

• A. \(x+y-1=0\)
• B. \(x-y-1=0\)
• C. \(x+y+1=0\)
• D. x-y+1=0

Hint:

For argument π/4, imaginary and real parts are equal.

Answer 1

The Correct Option is A

Step 1: Let z=x+iy. Then z-2-3i=(x-2)+i(y-3).
Step 2: Given arg(z-2-3i)=π/4, so (y-3)/(x-2)=1.
Step 3: Thus y-3=x-2 ⟹ x+y-1=0.