Question

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

Answer 1

`sqrt26(cos(0.197)+isin(0.197))`

Explanation:

To convert a complex number into trig form.

`color(red)(|bar(ul(color(white)(a/a)color(black)(x+yi=r(costheta+isintheta))color(white)(a/a)|)))`
where r is the magnitude and `theta` the argument.

Since( 5 + i) is in the 1st quadrant the the following formulae allow us to calculate r and `theta`

`•r=sqrt(x^2+y^2`

`•theta=tan^-1(y/x)`

here x = 5 and y = 1

`rArrr=sqrt(5^2+1^2)=sqrt26`

and `theta=tan^-1(1/5)=0.197" radians""or11.3^@`

`rArr5+i=sqrt26(cos(0.197)+isin(0.197))`