Question

Simplify: -27i^3 + 43i^7 - 8i^2 + 15i^3

A)
8 - 31i

B)
8 + 31i

C)
23 - 15i

D)
23 + 15i

Answer 1

First, combine like terms.

Answer 2

Then look at this:
\(i^0 = 1\)
\(i^1 = i\)
\(i^2 = -1\)
\(i^3 = -i\)
\(i^4 = 1\)
etc.

Answer 3

oh ok

Answer 4

@mathacomplice
Can you combine like terms and show what you get?

Answer 5

The only like terms are shown in red:

\(\large \color{red}{-27i^3} + 43i^7 - 8i^2 + \color{red}{15i^3}\)

Answer 6

so it'll be -12i^3?

Answer 7

Right.
Now you have this:

\(= -12i^3 + 43i^7 - 8i^2\)

Answer 8

Now use my table above, and replace i^3 by -i, i^2 by -1 and can you figure out what i^7 is equal to? To figure it out, just continue the pattern.

Answer 9

i, right?

Answer 10

No.
Notice that i^4 is the same as i^0.
Once you reach i^4, use i^0 and continue from there.

Answer 11

oh ok