Question A.4: Exponential Form of a Complex Number Express the complex num...

Conversion from polar to exponential forms is based on Equation A.13.
Thus, we have

A\underline{/\theta}=A \times (1\underline{/ \theta})=Ae^{j \theta} \quad \quad \quad \quad \quad (A.13) \\ Z=10 \underline{/60^\circ}=10e^{j60^\circ}

The rectangular form can be found by using Equation A.8:

\begin{matrix} e^{j \theta}&=&\cos(\theta)+j \sin(\theta) && \text{(A.8)} \\ Z&=&10 \times (e^{j60^\circ}) \\ &=&10 \times [\cos(60^\circ)+j\sin(60^\circ)] \\ &=&5+j8.66 \end{matrix}

The graphical representation of Z is shown in Figure A.6.