Given:
⇒ z2+|z|2=0
Let us assume z=x+iy
⇒ (x+iy)2 + \(\sqrt{(x^2+y^2)^2}\) = 0
⇒ x2+(iy)2+2(x)(iy)+x2+y2=0
⇒ 2x2+y2+i2y2+i2xy=0
We know that i2=-1
⇒ 2x2+y2-y2+i2xy=0
⇒ 2x2+i2xy=0
Equating Real and Imaginary parts on both sides we get,
⇒ 2x2=0 and 2xy=0
⇒ x=0 and y\(\varepsilon\)R
∴ z=0+iy where y\(\varepsilon\)R. i.e, Infinite solutions.