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

Question

7338 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-15T03:37:29

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

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

How do you convert 1 + 4i1 + 4i to polar form?