Can someone prove that rcis(θ) = r cis(θ +2kπ), where k ∈ Z.

[njc_]

hello,

I can’t understand how ‘rcis(θ)’ is supposed to be equivalent to ‘r cis(θ +2kπ)’ where k ∈ Z.

I read k ∈ Z to mean, k is any integer. Am I wrong? Or can I just not do math?

So, 3*cis(pi/3) is supposed to be equal to 3*cis(pi/3 + 2kpi) where k is any integer?

If anyone can help me here, I’d be very greatful.

Thank you.

 

[Dr.Peterson]

hello,

I can’t understand how ‘rcis(θ)’ is supposed to be equivalent to ‘r cis(θ +2kπ)’ where k ∈ Z.

I read k ∈ Z to mean, k is any integer. Am I wrong? Or can I just not do math?

So, 3*cis(pi/3) is supposed to be equal to 3*cis(pi/3 + 2kpi) where k is any integer?

If anyone can help me here, I’d be very greatful.

Thank you.

Since "cis(θ)" means "cos(θ) + i sin(θ)", and cos and sin both have period 2 pi, adding any integer multiple of 2 pi yields the same values. That's what a period means.