Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS4 Marks
Question
Convert the complex numbers given in Exercises in the polar form:
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Answer
Let $\text{r}\cos\theta=0$ and $\text{r}\sin\theta=1$ On squaring and adding, we obtain $\text{r}^2\cos^2\theta+\text{r}^2\sin^2\theta=0^2+1^2$ $\Rightarrow\ \text{r}^2(\cos^2\theta+\sin^2\theta)=1$ $\Rightarrow\ \text{r}^2=1$ $\Rightarrow\ \text{r}=\sqrt{1}=1$ [Conventionally, r > 0] $\therefore\ \cos\theta=0$ and $\sin\theta=1$ $\therefore\ \theta=\frac{\pi}{2}$ $\therefore\ \text{i}=\text{r}\cos\theta+\text{i r}\sin\theta=\cos\frac{\pi}{2}+\text{i}\sin\frac{\pi}{2}$ This is the required polar form.
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