complex numbers, polar form

[N K S]

The question says , cos 5Ѳ + i sin 5Ѳ = 1

How should i proceed to solve this?
Please help. Thanks in advance.

 

[pka]

The question says , cos 5Ѳ + i sin 5Ѳ = 1
How should i proceed to solve this?

\(\displaystyle \Theta=\dfrac{2k\pi}{5},~k\in\mathbb{Z}.\)

Are those solutions?

 

[Deleted member 4993]

The question says , cos 5Ѳ + i sin 5Ѳ = 1

How should i proceed to solve this?
Please help. Thanks in advance.

e^i(kΘ) = cos(kΘ) + i sin(kΘ)

 

[N K S]

\(\displaystyle \Theta=\dfrac{2k\pi}{5},~k\in\mathbb{Z}.\)

Are those solutions?

Hmm, nice. Thanks

 

[N K S]

e^i(kΘ) = cos(kΘ) + i sin(kΘ)

In this case , e ^i(5Θ) = 1
ln e^i(5Θ) = ln 1
i(5Θ) = 0


Next step ? :/

 

[Deleted member 4993]

In this case , e ^i(5Θ) = 1
ln e^i(5Θ) = ln 1
i(5Θ) = 0


Next step ? :/

e^i(5Θ) = 1

e^i(5Θ) = e^i(2kπ)

i(5Θ) = i(2kπ)

Θ = \(\displaystyle \dfrac{2k\pi}{5}\).............k = 0, 1, 2, 3.......