Question

Describe geometrically the set of points in the complex plane satisfying Re(z^2) = 4. Your |answer can be a qualitative description.

Answer 1

Answer with Step-by-step explanation:

let z= x+iy

Thus we have

$z^2=(x+iy)^2\\\\z^{2}=x^2+(iy)^2+2ixy\\\\z^2=x^2-y^2+2ixy\\\\Re(z^2)=x^2-y^2$

Thus for $Re(z^2)=4\\\\x^{2}-y^2=4\\\\\frac{x^2}{2^2}-\frac{y^2}{2^2}=1.........(i)$

Comparing the above equation with $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

The equation i above is equation of a hyperbola.