Calculus Problem

neon_glows

Im using text and tests to help me study for a college exam, in the ordinary level leaving cert book there is a qeustion:

Show that (1+i)^3 = -2 + 2i

My solution doent work prove this:

(1+i) (1+i)
= 1(1+i) + i(1+i)
= 1 + i + 1 + i
= 2 + 2i

now

(2 + 2i) (1 + i)
= 1(2+2i) + i(2+2i)
= 2 + 2i + 2i + 2i^2
= 2 + 4i + 2i^2
= 2 + 4i + 2(-1)
= 4i

Im really hoping this is an error in the book and me not completely messing up some fundamental complex number process.

LeixlipRed

You're wrong. (1 + i)^2 is equal to 2i. Then 2i times (1 + i) gives you -2 + 2i. The mistake you made is not squaring i in your first calculation. i^2 = -1. And you also multiplied i by 1 and got 1. Which is obviously wrong. Hope that helps

joe_chicken

neon_glows wrote:

Im using text and tests to help me study for a college exam, in the ordinary level leaving cert book there is a qeustion:

Show that (1+i)^3 = -2 + 2i

My solution doent work prove this:

(1+i) (1+i)
= 1(1+i) + i(1+i)

= 1 + i + i -1 ...(i*i = -1)

= 2i

2i(1+i) = 2i - 2 ... done

/EDIT... too slow

neon_glows

thanks guys, makes more sense now.