Find the product of (5+10i) and its conjugate

Question

Complex numbers

Answer 1

(a-b)(a+b) = a²-b² (the expression on the right is called a difference of squares--which results any time we multiply the sum and difference of the same two "numbers").

When you multiply complex conjugates the result is a difference of squares which has the effect of removing the "i" or imaginary part of the complex number (because i²=-1). When you multiply complex conjugates, the result is a real number.

For the complex number 5+10i its conjugate is 5 - 10i. Simply apply the formula to reach a difference of squares:

5² - (10i)² = 25 - (100i²) = 25 - (-100) = 25 + 100 = 125.