IM Alg2.3.13 Lesson: Multiplying Complex Numbers
Write each expression in the form a+bi, where a and b are real numbers.
Take turns with your partner to match an expression in column A with an equivalent expression in column B.
- For each match that you find, explain to your partner how you know it’s a match.
- For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
Write each product in the form a+bi, where a and b are real numbers.
On October 16, 1843, while walking across the Broom Bridge in Dublin, Ireland, Sir William Rowan Hamilton came up with an idea for numbers that would work sort of like complex numbers. Instead of just the number (and its opposite) squaring to give -1, he imagined three numbers , , and (each with an opposite) that squared to give -1. The way these numbers multiplied with each other was very interesting. times would give , times would give , and times would give . But the multiplication he imagined did not have a commutative property. When those numbers were multiplied in the opposite order, they’d give the opposite number. So times would give , times would give , and times would give . A quaternion is a number that can be written in the form where , , , and are real numbers. Let and . Write each given expression in the form .