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- #1

- Jan 26, 2012

- 4,055

**soroban**for proposing this problem!

\(\displaystyle \left| (1+2i)^n \right|^2\) for n=1,2,3... can be generalized in a very simple form that doesn't include any notation related to complex numbers.

1) Find a way to generalize the nth term.

2) Prove your generalization is valid

Hint 1:

For $n \ge 2$ you'll have to simplify $(1+2i)^n$ to the form of $a+bi$ and then calculate $a^2+b^2$.

Hint 2:

If this problem seems too tricky for you then I suggest reading up on complex numbers, focusing on multiplying them and finding the magnitude.

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