Question

Algebra of complex number equality of two complex number​

Answer 1

Two complex numbers z1 = a + ib and z2 = x + iy are equal if and only if a = x and b = y i.e., Re (z1) = Re (z2) and Im (z1) = Im (z2).

Thus, z1 = z2 ⇔ Re (z1) = Re (z2) and Im (z1) = Im (z2).

For example, if the complex numbers z1 = x + iy and z2 = -5 + 7i are equal, then x = -5 and y = 7.