MATH SOLVE

5 months ago

Q:
# What is each power of i with its multiplicative inverse.1. i 2. i ^2 3. i ^3 4. i ^4

Accepted Solution

A:

Answer:1) multiplicative inverse of i = -i2) Multiplicative inverse of i^2 = -13) Multiplicative inverse of i^3 = i4) Multiplicative inverse of i^4 = 1Step-by-step explanation:We have to find multiplicative inverse of each of the following.1) iThe multiplicative inverse is 1/iif i is in the denominator we find their conjugate[tex]=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i[/tex]So, multiplicative inverse of i = -i2) i^2The multiplicative inverse is 1/i^2We know that i^2 = -11/-1 = -1so, Multiplicative inverse of i^2 = -13) i^3The multiplicative inverse is 1/i^3We know that i^2 = -1and i^3 = i.i^2[tex]1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i[/tex]so, Multiplicative inverse of i^3 = i4) i^4The multiplicative inverse is 1/i^4We know that i^2 = -1and i^4 = i^2.i^2[tex]=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1[/tex]so, Multiplicative inverse of i^4 = 1