- In order to analyze AC circuit, it is necessary to represent multi-dimensional quantities. In order to accomplish this task, scalar numbers were abandoned and complete numbers were used to express the two dimensions of frequency and phase shift at one time
- In mathematics, ‘i’ is used to represent imaginary numbers. In the study of electricity and electronics, j is used to represent imaginary numbers so that there is no confusion with I, which in electronics represents current (i). It is also customary for scientist to write the complex number in the form of a + jb.
1. A complex number may be written in Rectangular form as:
\(Z=X+jY.\)
where X = r cos(θ) is real and Y = r sin(θ) is imaginary number.
θ = tan-1 (Y/X).
2. A second way of representing the complex number is by specifying the magnitude(r) and angle (θ) in polar form
Z = r ∠θ;
\(r=\sqrt{X^2+Y^2}; \theta=tan^{-1}(Y/X).\)
3. The third way of representing the complex number is the Exponential form.
\(Z=re^{j\theta}\,,\theta=tan^{-1}(\frac{Y}{X}),\,r=\sqrt{X^2+Y^2}\)
