Question

How do you write the complex number in trigonometric form `5/2(sqrt3-i)`?

Answer 1

In trigonometric form expressed as `5(cos330+isin330)`

Explanation:

`Z=a+ib`. Modulus: `|Z|=sqrt (a^2+b^2)`; Argument:`theta=tan^-1(b/a)` Trigonometrical form : `Z =|Z|(costheta+isintheta)`
`Z=5/2(sqrt3-i)= 5/2sqrt3 -5/2i`. Modulus `|Z|=sqrt(( 5/2sqrt3 )^2+(-5/2)^2) =sqrt(75/4+25/4)=sqrt25=5`
Argument: `tan theta= (-cancel(5/2))/(cancel(5/2)sqrt3)= -1/sqrt3`. Z lies on fourth quadrant, so `theta =tan^-1(-1/sqrt3) = -pi/6=-30^0 or theta = 360-30=330^0 :. Z=5(cos330+isin330)`
In trigonometric form expressed as `5(cos330+isin330)`[Ans]