Aim: How do we multiply or divide complex numbers? Do Now: 6 + 7x + 2x2 1. Multiply: 2. Multiply: 4 + 7i 3. Multiply:

Multiplying Treat the i’s like variables, then change any i2 to -1 Ex: Ex: Remember: The product of two complex numbers is a complex number

Complex Conjugate The conjugate of the complex number a + bi is the complex number a – bi. For example, the conjugate of 5 + 2i is 5 – 2i. Similarly, 3 – i and 3 + i are conjugates to each other. The product of two complex numbers that are conjugates is a real number

Divide 8 + i by 2 – i Write the division problem in fractional form Multiply the conjugate of the denominator, and the numerator also multiply accordingly Multiply the binomials and combine the like terms Simplify Simplify and write the result in the form of a + bi

Write the multiplicative inverse of 2 + 4i in the form of a + bi Rationalize the denominator by multiplying the conjugate of the denominator on both the numerator and denominator Multiply Simplify: Simplify and write the result in a + bi form

Drill: 1. Multiply: 5 – 15i 2. Multiply: (3 – 2i)(3+2i) 13 3. Divide: 5. Write the multiplicative inverse of 9 – 2i in the a + bi form