show that the product of a + bi and its conjugate is real number?

Answer 1

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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.

Answer 2

a+bi(a-bi)=a^2+b therefore its a real number

Source(s): no1 is special every1 is