Question

What is the trigonometric form of `(-7+2i)`?

Answer 1

`sqrt53(cos(2.86)+isin(2.86))`

Explanation:

To convert from `color(blue)"standard to trigonometric form"`

`"that is "(x,y)tor(costheta+isintheta)`

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

`"and " color(red)(bar(ul(|color(white)(2/2)color(black)(theta=tan^-1(y/x))color(white)(2/2)|)))`
`color(white)(xxxx)"where" -pi < theta<=pi`

`"here " x=-7" and "y=2`

`rArrr=sqrt((-7)^2+2^2)=sqrt53`

`"Since "-7+2i` is in the second quadrant, we must ensure that `theta` is in the second quadrant.

`theta=pi-tan^-1(2/7)`

`rArrtheta=(pi-0.278)=2.86larr" in second quadrant"`

`rArr-7+2itosqrt53(cos(2.86)+isin(2.86))`