WebbSuppose complex number z = a + bi z = a+bi is a solution to this equation, and consider the polar representation z = r e^ {i\theta} z = reiθ, where r = \sqrt {a^2 + b^2} r = a2 +b2 and \tan \theta = \frac {b} {a}, 0 \leq \theta < 2\pi tanθ = ab,0 ≤ θ < 2π. Then, by De Moivre's … WebbPROPERTIES OF COMPLEX NUMBERS 1. The product of a complex number and its conjugate is a real number. Proof : (a + ib) and (a - ib) are two complex numbers conjugate to each other, where a and b are real numbers. (a + ib) (a - ib) = a2 - (ib)2 = a2 - i2b2 = a2 - (-1)b2 = a2 + b2 (real number) 2.
Properties of Complex Numbers are explained with Proof.
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