Question

How do you write the complex number in trigonometric form `5-12i`?

Answer 1

In trigonometric form : `13(cos292.62+isin292.62)`

Explanation:

`Z=a+ib`. Modulus: `|Z|=sqrt (a^2+b^2)`; Argument:`theta=tan^-1(b/a)` Trigonometrical form : `Z =|Z|(costheta+isintheta)`

`Z=5-12i`. Modulus `|Z|=sqrt(5^2+(-12)^2) =sqrt(25+144)=sqrt169=13`

Argument: `tan alpha = 12/5= 2.4`. Z lies on fourth quadrant, `alpha =tan^-1(2.4) = 67.38^0 :. theta = 360-67.38=292.62^0 :. Z=13(cos292.62+isin292.62)`

In trigonometric form expressed as `13(cos292.62+isin292.62)` [Ans]