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Question

The complex number z satisfying the equation |z|=z+1+2i is


Correct Answer
A
322i
Your Answer
B
32+2i
Your Answer
C
232i
Your Answer
D
32i2

Solution

The correct option is A 322i
Let z=x+iy
Given that |z|=z+1+2i
x2+y2=x+iy+1+2i
x2+y2=(x+1)+(2+y)i 
On comparing real and imaginary parts,
x2+y2=x+1
and 0=2+yy=2
x2+4=x+1
x2+4=x2+2x+1
2x=3
x=32
z=x+iy=322i

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