(2+3i)(2-3i) = 2²-(3i)² = 4-9i² = 4-9(-1) = 4+9 = 13. The product of a complex number and its conjugate always gives a real number equal to ...
(2+3i)(2-3i) = 2²-(3i)² = 4-9i² = 4-9(-1) = 4+9 = 13. The product of a complex number and its conjugate always gives a real number equal to sum of squares of real and imaginary parts. This property is used to rationalize complex denominators when dividing complex numbers.