CBSE Class 11-science Answered
Convert the complex number
in to polar form.
![](http://images.topperlearning.com/topper/questions/4483_image050.gif)
Asked by Topperlearning User | 25 Apr, 2014, 09:52: AM
We can simplify the given complex number in form as follows:
![](https://images.topperlearning.com/topper/questions/4483_image052.gif)
Let, ![](https://images.topperlearning.com/topper/questions/4483_image053.gif)
![](https://images.topperlearning.com/topper/questions/4483_image053.gif)
Equating real and imaginary parts of both sides, we get,
![](https://images.topperlearning.com/topper/questions/4483_image054.gif)
Squaring and adding, we get,
![](https://images.topperlearning.com/topper/questions/4483_image055.gif)
Hence, putting the value of r in equation (1) and (2), we get,
![](https://images.topperlearning.com/topper/questions/4483_image056.gif)
Now the value of
such that
and satisfy the above equation is given by ![](https://images.topperlearning.com/topper/questions/4483_image057.gif)
![theta](https://images.topperlearning.com/topper/tinymce/cache/31c361c3cc58cdb507dd0c1c79aeb1ac.png)
![](https://images.topperlearning.com/topper/questions/4483_image046.gif)
![](https://images.topperlearning.com/topper/questions/4483_image057.gif)
Hence, ![](https://images.topperlearning.com/topper/questions/4483_image058.gif)
![](https://images.topperlearning.com/topper/questions/4483_image058.gif)
Which is the required polar form.
Answered by | 25 Apr, 2014, 11:52: AM
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