Question

Find all complex numbers which make the following equations true
|z+ 1|=1 and |z^2+ 1| = 1​

Answer 1

Answer:

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Step-by-step explanation:

We have, ∣∣∣∣zzz2+z2∣∣∣∣=1

Let z=x+iy, and we know zz=1

∴∣z2+z2∣=1⇒∣x2−y2∣=21

and it's given that, x2+y2=1

∴2x2=23⇒x=±23

And y=±21

Therefore, Number of complex numbers z are 4