Question

How do you write `2 +4i` in trigonometric form?

Answer 1

`2sqrt5(cos(1.107)+isin(1.107))`

Explanation:

`"to convert to trigonometric form"`

`"that is "x+yitor(costheta+isintheta)" using"`

`•color(white)(x)r=sqrt(x^2+y^2)`

`•color(white)(x)theta=tan^-1(y/x);-pi < theta <=pi`

`"here "x=2" and "y=4`

`rArrr=sqrt(2^2+4^2)=sqrt20=2sqrt5`

`theta=tan^-1(2)=1.107" radians to 3 dec. places"`

`rArr2+4i=2sqrt5(cos(1.107)+isin(1.107))`