Question

Find the product of -1 + 3i and its conjugate. The answer is a + bi where

The real number a equals
The real number b equals

Answer 1

`\huge\boxed{a = 10 \ , \ b = 0}`

Explanation:

Conjugate of -1 + 3i = -1 - 3i

Their Product:

`=(-1+3i)(-1-3i)\\Using \ Formula : (a+b)(a-b) = a^2-b^2\\=(-1)^2 - (3i)^2\\=1 - 9i^2\\We \ know \ that \ i^2 = -1\\=1 - 9(-1)\\=1 + 9\\=10`

Since the answer is 10, It seems like:

a + bi = 10

So, This means that:

a = 10

b = 0