Question

How do you convert `1 + 4i` to polar form?

Answer 1

`~=sqrt(17)(cos1.33 + isin1.33)`

Explanation:

If `z = a +bi`

Then `z` may be expressed in polar form as:

`z = r(cos theta + i sin theta)`
Where: `r = sqrt(a^2 + b^2)` and `theta = arctan(b/a)`

In this example: `z=1+4i`
Hence: `a=1` and `b=4`

Therefore: `r = sqrt(1^2+4^2)` =`sqrt(17)`
And: `theta = arctan(4/1)` `~= 1.33`

Hence: `z ~= sqrt(17)(cos 1.33 + i sin 1.33)`