Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS4 Marks
Question
Convert the complex numbers given in Exercises in the polar form: -3.
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Answer
Given: $\text{z}=\text{r}(\cos\theta+\text{i}\sin\theta)=-3$$\therefore\ \text{r}\cos\theta=-3$ and $\text{r}\sin\theta=0$
Squaring both sides and adding both the equations, we get
$\text{r}^2(\cos^2\theta+\sin^2\theta)=9+0$
$\Rightarrow\ \text{r}^2=9\Rightarrow\ \text{r}=3$
$\therefore\ 3\cos\theta=-3$ and $3\sin\theta=0$
$\Rightarrow\ \cos\theta=-1$ and $\sin\theta=0$
$[\theta$ lies in second quadrant$]$
$\therefore\ \theta=(\pi-0)=\pi$
Therefore, polar form of z is $3[\cos\pi+\text{i}\sin\pi].$
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