# For 12i^12 + pi(i) was if the imaginary and what is the real part?

Jun 6, 2018

Real: $1$
Imaginary: $\pi$

#### Explanation:

Calculate the powers of $i$:
${i}^{1} = i$
${i}^{2} = - 1$
${i}^{3} = - i$
${i}^{4} = 1$

We see that this cycles around, with ${i}^{n + 4} = {i}^{n}$ for all $n$. So ${i}^{12} = 1$.

Thus $12 {i}^{12} + \pi i = 1 + i \pi$, with real part $1$ and imaginary part $\pi$.