Question

How do you find the real and imaginary part `12i^12 + pi(i)`?

Answer 1

`12i^12=12` is real. `pii` is imaginary.

Explanation:

Note that we can simplify `i^12`:

`{(i=color(red)(sqrt(-1))),(i^2=(color(red)(sqrt(-1)))^2=color(blue)(-1)),(i^4=(i^2)^2=(color(blue)(-1))^2=color(green)1),(i^12=(i^4)^3=color(green)1^3=1):}`

Thus, the expression simplifies to be:

`12i^12+pii=12(1)+pii=12+pii`

This is a complex number in the form

`a+bi`

where `a=12` and `b=pi`. Since `pi` is multiplied by `i`, the imaginary unit, `pii` is the imaginary part of the expression. So, `12i^12=12` is the real part.