CBSE Class 11-science Answered
Find the polar form of complex number
![](http://images.topperlearning.com/topper/questions/4479_image009.gif)
Asked by Topperlearning User | 11 Aug, 2014, 10:03: AM
![](https://images.topperlearning.com/topper/questions/4479_image011.gif)
Now, Let, ![](https://images.topperlearning.com/topper/questions/4479_image012.gif)
![](https://images.topperlearning.com/topper/questions/4479_image012.gif)
Equating real and imaginary parts, we get,
![](https://images.topperlearning.com/topper/questions/4479_image013.gif)
Squaring and adding, we get
![1 plus 1 equals r squared cos space squared space theta space plus space r squared space sin to the power of space 2 end exponent space theta](https://images.topperlearning.com/topper/tinymce/cache/d4d4044b0a6338f5f8eddae798db2edc.png)
![](https://images.topperlearning.com/topper/questions/4479_image015.gif)
Now putting the value of r in equations (1)
![](https://images.topperlearning.com/topper/questions/4479_image016.gif)
![](https://images.topperlearning.com/topper/questions/4479_image017.gif)
Now the value of
such that
and satisfying both above equations is given by ![](https://images.topperlearning.com/topper/questions/4479_image018.gif)
![theta](https://images.topperlearning.com/topper/tinymce/cache/31c361c3cc58cdb507dd0c1c79aeb1ac.png)
![](https://images.topperlearning.com/topper/questions/4479_image006.gif)
![](https://images.topperlearning.com/topper/questions/4479_image018.gif)
Hence,
![](https://images.topperlearning.com/topper/questions/4479_image019.gif)
Which is the required polar form.
Answered by | 11 Aug, 2014, 12:03: PM
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