Basic Technical Mathematics, 11th Edition

12.5 Exponential Form of a Complex Number

• Exponential Form $\mathit{r}{\mathit{e}}^{\mathit{j}\mathit{\theta }}$ • Expressing Numbers in Exponential Form • Summary of Important Forms

Another important form of a complex number is the exponential form. It is commonly used in electronics, engineering, and physics applications. As we will see in the next section, it is also convenient for multiplication and division of complex numbers, as the rectangular form is for addition and subtraction.

The exponential form of a complex number is written as $r{e}^{j\theta }\hspace{0.17em},\hspace{0.17em}$ where r and $\theta$ have the same meanings as given in the previous section, although $\theta$ is expressed in radians. The number e is a special irrational number and has an approximate value

$$e\hspace{0.17em}=\hspace{0.17em}2.7182818284590452$$

The number e is named for the Swiss mathematician ...