Answer:
see explanation
Step-by-step 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:
a^2 + b^2
Step-by-step 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
