For $12 i^{12} + π (i)$ $12i^12 + pi(i)$ was if the imaginary and what is the real part?

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Answer 1 · 2018-06-06T20:31:58

Real: $1$ $1$
Imaginary: $π$ $pi$

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

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

Thus $12 i^{12} + π i = 1 + i π$ $12i^(12)+pi i=1+ipi$ , with real part $1$ $1$ and imaginary part $π$ $pi$ .

For 12i12+π(i)12i^12 + pi(i) was if the imaginary and what is the real part?