Solve for z, the equation |z|+ z = 2 + i

Z=a+ib

IzI + Z =2 + i

Ia+ibI + a+ib = 2+ i

(a2 + b2)1/2 + a+ib = 2+i

(a2 + b2)1/2 = 2 + i - a - ib

= (2-a) + (i-ib)

= (2-i) + i(1-b)

Comparing real and imaginary parts,

(a2 +b2)1/2 = 2-a 1-b=0

(a2 + 1)1/2 = 2-a b=1

a2 +1 = (2-a)2 = 4 + a2 - 4a

-4a = 1-4

a = 3/4

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Please show answer 3/4+i
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