show that the product of a + bi and its conjugate is real number?
- 1 decade agoFavorite Answer
By definition, the conjugate of a + bi is a - bi.
(a + bi)(a - bi) = a^2 - abi + abi - (bi)^2 = a^2 - (bi)^2
= a^2 - (b^2)( i^2) = a^2 - (-1)(b^2) since i^2 = -1
= a^2 + b^2
If a and b are real, then a^2 + b^2 is also real.
- 1 decade ago
a+bi(a-bi)=a^2+b therefore its a real numberSource(s): no1 is special every1 is