# 12.4 Polar Form of a Complex Number

**Polar Form**$\mathit{r}\mathbf{(\hspace{0.17em}}\mathbf{cos}\mathit{\text{}}\mathbf{\theta}\mathbf{\text{}}\mathbf{+\hspace{0.17em}}\mathbf{\text{}}\mathit{j}\mathbf{\text{}}\mathbf{sin}\mathbf{\text{}}\mathit{\theta}\mathbf{)\hspace{0.17em}}$ •**Expressing Numbers in Polar Form**

In this section, we use the fact that a complex number can be represented by a vector to write complex numbers in another form. This form has advantages when multiplying and dividing complex numbers, and we will discuss these operations later in this chapter.

In the complex plane, by drawing a vector from the origin to the point that represents the number $x\hspace{0.17em}+\hspace{0.17em}yj\hspace{0.17em},\hspace{0.17em}$ an angle $\theta $ in standard position is formed. The point $x\hspace{0.17em}+\hspace{0.17em}yj$ is `r` units from the origin. In fact, *we can find any point in the complex plane by knowing the angle* $\theta $ *and the value of r*. The equations relating

`x, y, r,`and $\theta $ are similar to those developed for vectors in Chapter

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