Multiplying Complex Numbers

This podcast explains how to multiply complex numbers using various methods, including foiling and simplifying expressions involving imaginary numbers. It demonstrates how to remove imaginary numbers from denominators using techniques such as multiplying by the conjugate and illustrates how to express answers in standard complex number form (a + bi).

Multiplying Complex Numbers

• 00:00:08 The podcast begins by demonstrating how to multiply a complex number by itself, such as (-4i)^2, using the property i^2 = -1. This is followed by demonstrating how to foil two complex numbers, like (9-7i)(-6-5i), and then combine real and imaginary terms to arrive at a simplified solution in the form a + bi.

Dividing Complex Numbers

• 00:01:43 The podcast then tackles division of complex numbers, where the goal is to remove the imaginary number from the denominator. The speaker explains how to achieve this by multiplying the numerator and denominator by the conjugate of the denominator, leading to a simplified answer. The podcast also shows an example where multiplying by -i creates a positive denominator.