Question

Evaluate the expression (-4+4i)(1+4i)(1+4i) and write the result in the form a+bi

Answer 1

Explanation:

Since 2 of the 3 binomials are identical I would start the distribution there.

(1 + 4i)(1 + 4i) =
`1+8i+16i^2`

I'm sure you have learned in class by now that i-squared is = to -1, so we can make that substitution:

1 + 8i + 16(-1) which simpifies to

1 + 8i - 16 which simplifies further to

-15 + 8i. Now we need to FOIL in the last binomial:

(-15 + 8i)(-4 + 4i) =
`60-60i-32i+32i^2`

Combine like terms to get

`60-92i+32i^2`

Again make the substitution of i-squared = -1:

60 - 92i + 32(-1) which simplifies to

60 - 92i - 32 which simpifies, finally, to a solution of:

28 - 92i