Question

Find the multiplicative inverse of z=-4+√2i

Answer 1

If z is any complex number the 1/z is called the multiplicative inverse of z.

Given that

z = -4+√2i

So 1/z = 1/(-4+√2i)

1/z = [1/(-4+√2i)]×[(-4-√2i)/(-4-√2i)]         [ on rationalizing]

1/z = (-4-√2i)/(16-2i²)                                [ a²-b²=(a+b)(a-b) ]                

1/z = (-4-√2i)/(16+2)                                  [ i² = -1 ]

1/z = (-4-√2i)/18

Hence multiplicative inverse of -4+√2i is (-4-√2i)/18