Trigonometric Form of a Complex Number...5

[nycmathguy]

Section 6.6

More precalculus later today.

 

[MathLover1]

correct

 

[nycmathguy]

correct

Can you do 14 ad 16?

 

[MathLover1]

14.
z=4
z=a+bi=4-> a=4, b=0
|z|=sqrt(4^2+0^2)=4

tan(θ)=0/4=0
θ=tan^-1(0)
θ=0 radians or 0°

z=4(cos(0)+i*sin(0))


16.
3-i -> a=3, b=-1
|z|=sqrt(3^2+(-1)^2)=sqrt(10)
tan(θ)=-1/3
θ=tan^-1(-1/3)
θ=-0.32175

z=sqrt(10)(cos(-0.32175)+i*sin(-0.32175))

 

[nycmathguy]

14.
z=4
z=a+bi=4-> a=4, b=0
|z|=sqrt(4^2+0^2)=4

tan(θ)=0/4=0
θ=tan^-1(0)
θ=0 radians or 0°

z=4(cos(0)+i*sin(0))


16.
3-i -> a=3, b=-1
|z|=sqrt(3^2+(-1)^2)=sqrt(10)
tan(θ)=-1/3
θ=tan^-1(-1/3)
θ=-0.32175

z=sqrt(10)(cos(-0.32175)+i*sin(-0.32175))

Ok. Cool. By the way, my roommate just informed me that he took off from work this weekend. When he's home, it's really hard to concentrate on math. I will do my best finish the current section this weekend.

After Section 6.6, we move on to Chapter 10 to complete our precalculus journey. Chapters 7, 8, and 9 is just a review of college algebra. I downloaded a college algebra textbook for a future study.