Question

What is the trigonometric form of `(2+5i)`?

Answer 1

`sqrt29 /_1.19`

Explanation:

Any complex number `z=x+iy` in rectangular form, may be written in polar form `z=r/_theta` by making use of the transformations:
`r=sqrt(x^2+y^2)and theta=tan^(-1)(y/x), theta in [-pi,pi]`.

So in this particular case, since the complex number is in the first quadrant of the argand plane, we get:

`r=sqrt(2^2+5^2)=sqrt29`

`theta=tan^(-1)(5/2)=68,2^@=1.19rad`.

Thus the point may be represented as `sqrt29 /_1.19`