Question

How do you write the complex number in trigonometric form `4`?

Answer 1

`4(cos0+isin0)`

Explanation:

To express a complex number in trigonometric form.

`color(red)(|bar(ul(color(white)(a/a)color(black)(z=x+yi=r(costheta+isintheta))color(white)(a/a)|)))`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(r=sqrt(x^2+y^2))color(white)(a/a)|)))`

`color(red)(|bar(ul(color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|)))`

consider `z=4=4+0i`

here x = 4 and y = 0

`rArrr=sqrt(4^2+0^2)=4`

and `theta=tan^-1(0/4)=tan^-1(0)=0`

`rArrz=4=4(cos0+isin0)" in trigonometric form"`