[MOVED] Evaluate K = 1 + 2i + 3i^2 + 4i^3 + 5i^4 + 6i^5 +...

[Guest]

Evaluate K = 1 + 2i + 3i^2 + 4i^3 + 5i^4 + 6i^5 + ....+ 100i^99 given that i^2 = -1.

I dont know where to start with this one...

 

[skeeter]

i¹ = i
i² = -1
i³ = -i
i⁴ = 1
i⁵ = i
i⁶ = -1
i⁷ = -i
i⁸ = 1
and so on ... see the pattern?

so ... your series is

1 + 2i - 3 - 4i + 5 + 6i + ... - 100i

this can be broken up into two series ...

1 - 3 + 5 - 7 + 9 - 11 + ... + 97 - 99 = ?

and

2i - 4i + 6i - 8i + 10i - 12i + ... + 98i - 100i = ?

can you proceed?

 

[stapel]

I dont know where to start with this one...

Are you not familiar with the "imaginary" number "i"?

Thank you.

Eliz.