Question

The product of a complex number and its complex

conjugate is
a real number.
(a+bi)(a - bi) = a? – (biº) = a + b2

Answer 1

see explanation

Explanation:

Given a complex number a + bi and its conjugate a - bi , a, b ∈ R, then the product is

(a + bi)(a - bi) ← expand using FOIL

= a² - abi + abi - b²i² [ i² = - 1 ]

= a² - b²(- 1)

= a² + b² ← a real number

Answer 2

a^2 + b^2

Explanation:

The product of a complex number and its complex

conjugate is

a real number.

(a+bi)(a - bi)

Recall the formula for the product of a binomial and its conjugate:

(a + b)(a - b) = a^2 - B^2

Then:

The product of a complex number and its complex

conjugate is

a real number.

(a+bi)(a - bi) = a^2 - (bi)^2 = a^2 - b^2(-1) = a^2 + b^2