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Question

If z2z+2(z2) is purely imaginary then |z| is equal to
  1. 1
  2. 3
  3. 4
  4. 2

A
1
B
2
C
4
D
3
Solution
Verified by Toppr

Let z=x+iy
Then, z2z+2=x+iy2x+iy+2=(x2)+iy(x+2)+iy
=[(x2)+iy][(x+2)+iy](x+2)2+y2
=(x2+y24)+i(4y)(x+2)2+y2
Since z2z+2 is purely imaginary,
x2+y24=0
x2+y2=4|z|2=4|z|=2.

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