Question

If `z=((sqrt(3)+i)^(17))/((1-i)^(50))` , then find `a m p(z)dot`

Answer 1

`((sqrt(3+i))^(17))/((1-i))^(50) = ((2(sqrt(3)/(2) +(i)/(2)))^(17))/((sqrt(2)((1)/(sqrt(2))-(i)/(sqrt(2))))^(50))`
`rArr agr(z) = 17 arg (sqrt(3)/(2)+(i)/(2))-50 arg((1)/(sqrt(2))-(i)/(sqrt(2)))`
`= 17((pi)/(6)) - 50 (-(pi)/(4))`
`= (17pi)/(6) + (25)/(2) = (46pi)/(3) = 15 pi+ (pi)/(3)`
Thus, lies in thrid quadrant with principal argument `- pi + (pi)/(3) = - (2pi)/(3)`