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Question

Let z be a complex number such that |z|+z=3+i (where i=1). Then |z| is equal to :


A
53
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B
54
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C
343
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D
414 
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Solution

The correct option is A 53
|z|+z=3+i     (1)
Let z=x+iy
|z|=x2+y2
From equation (1)
x2+y2+x+iy=3+i(x2+y2+x)+iy=3+iy=1x2+1+x=3x2+1=3xx2+1=(3x)2x=43

Thus, |z|=x2+y2
              =(43)2+(1)2
              =53

Mathematics

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