Question

How do you write the trigonometric form of `1+3i`?

Answer 1

`sqrt10(cos1.249+isin1.249)`

Explanation:

`"to convert to "color(blue)"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=1" and "y=3`

`rArrr=sqrt(1^2+3^2)=sqrt10`

`theta=tan^-1(3)=1.249" radians"`

`rArr1+3itosqrt10(cos1.249+isin1.249)`