Complex Number Help!

[Damo17]

I'm having trouble working out one question:

If n is an even natural number show that  (-1)^n/2 = i^n

(Don't know how to use latex)

[perfectscore]

y are u doing complex no.s now?

[Mao]

y are u doing complex no.s now?

because he's doing unit 1/2

[Damo17]

We just started it in General Maths Advanced, but it's so basic and i've finished the chapter already so I've gone onto next years (Specialist) complex numbers chapter to pose a challenge to me.

[Mao]

I'm having trouble working out one question:

If n is an even natural number show that  (-1)^n/2 = i^n

(Don't know how to use latex)

did you mean:

Code: [Select]

[tex](-1)^{\frac{n}{2}}=i^{n}[/tex]

or

Code: [Select]

[tex]\frac{(-1)^{n}}{2}=i^{n}[/tex]


[enwiabe]

i = sqrt(-1)
i^2 = (sqrt(-1))^2 = -1

Therefore,
(-1)^(n/2) = (i^2)^(n/2) = i^(2*n/2) = i^n as required.

I, too, am latex-challenged.

[Collin Li]

He would have meant the first one, Mao.

[Mao]

i = sqrt(-1)
i^2 = (sqrt(-1))^2 = -1

Therefore,
(-1)^(n/2) = (i^2)^(n/2) = i^(2*n/2) = i^n as required.

I, too, am latex-challenged.

you are a disgrace

he meant:



Therefore,
as required.

[Damo17]

He would have meant the first one, Mao.

Yeah, the first one.

Thanks, I get it now.

[Mao]

on a side note, it is true that , not only limited to even integers, since the definition of the imaginary number is

[Damo17]

on a side note, it is true that , not only limited to even integers, since the definition of the imaginary number is

Great, I'm loving learning this, it's a bit harder than unit 1/2 but so much more interesting.

[Damo17]

Another question i'm finding hard.

If find the values of and such that 

[Mao]

so, equating real/imag parts:

imaginary:






real:

[dcc]

Therefore,
as required.

on a side note, it is true that , not only limited to even integers, since the definition of the imaginary number is

[Damo17]

Thanks Mao, got it now.
It all seems so easy when you show it like that, doing it so quickly.