Trigonometric Form of a Complex Number...4

[nycmathguy]

Section 6.6

 

[MathLover1]

10.

(5/2)(sqrt(3)-i)
=(5/2)sqrt(3)-(5/2)i

r=sqrt(((5/2)sqrt(3))^2+(5/2)^2)=5

tan(θ)=(5/2)/(sqrt(3))(5/2)=1/sqrt(3)

θ=tan^-1(1/sqrt(3))

θ=π/6

5(cos(-π/6)+i*sin(-π/6))

22.
3sqrt(2)-7i

r=sqrt((3sqrt(2))^2+7^2)=sqrt(67)

tan(θ)=7/(3sqrt(2))
θ=tan^-1(7/(3sqrt(2)))
θ=1.02591
or
θ=58.78°

z=sqrt(67)(cos(1.02591)+i*sin(1.02591))
or
z=sqrt(67)(cos(58.78°)+i*sin(58.78°))

 

[nycmathguy]

10.

(5/2)(sqrt(3)-i)
=(5/2)sqrt(3)-(5/2)i

r=sqrt(((5/2)sqrt(3))^2+(5/2)^2)=5

tan(θ)=(5/2)/(sqrt(3))(5/2)=1/sqrt(3)

θ=tan^-1(1/sqrt(3))

θ=π/6

5(cos(-π/6)+i*sin(-π/6))

22.
3sqrt(2)-7i

r=sqrt((3sqrt(2))^2+7^2)=sqrt(67)

tan(θ)=7/(3sqrt(2))
θ=tan^-1(7/(3sqrt(2)))
θ=1.02591
or
θ=58.78°

z=sqrt(67)(cos(1.02591)+i*sin(1.02591))
or
z=sqrt(67)(cos(58.78°)+i*sin(58.78°))

I got both wrong. . .again?