Mathematical Operations of Complex Numbers:
Assume \(Z_{1}=X_{1}+jY_{1}\)
or \(r_{1}\angle\theta_{1}and\,Z_{2}=X_{2}+Y_{2}\,or\,r_{2}\angle\theta_{2}\,\)
are two complex numbers
Addition: \(Z_{1}+Z_{2}=(X_{1}+X_{2})+j(Y_{1}+Y_{2})\)
Subtraction: \(Z_{1}-Z_{2}=(X_{1}-X_{2})+j(Y_{1}-Y_{2})\)
Multiplication: \(Z_{1}Z_{2}=r_{1}r_{2}\angle(\theta_{1}+\theta_{2})\)
Division: \(Z_{1}/Z_{2}=(r_{1}/r_{2})\angle(\theta_{1}-\theta_{2})\)
Reciprocal: \(1/Z_{1}=(1/r_{1})\angle-\theta_{1}\)
Square root: \(\sqrt{Z_{1}}=\sqrt{r_{1}}\angle\frac{\theta_{1}}{2}\)
Complex Conjugate: \(Z^*=X-jY=\sqrt{r}\angle\theta=re^{-j\theta}\)
