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Question

Solve |z| + z = 2 + i , where z is a complex number.?


Solution


|z| + z = 2 + i
Let z = x + iy
|z|+x+iy=2+i
Equating imaginary part, \rightarrow y = 1
Equating real part,
x2+y2+x=2x2+1+x=2x2+1=(2x)Squaring,x2+1=4+x24x34x=0 or x=43

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