Complex Numbers

Numbers that are not real are called Imaginary. They use the letter i.

i = √-1 or i2 = -1

Simplify each:√-81 √-10 √-32 √-810

A Complex Number is a number that has both a Real and an Imaginary component.

Written in the form a + bia is the REAL number bi is the IMAGINARY number

To add, subtract, or multiply complex numbers, just treat them like binomials.

Don’t forget… i2 = -1

1. (6 + 4i) + (-2 – 2i) 2. (-14 + 2i) – (6 + i) + (19 +

10i) 3. (4i)(-7i) 4. (6 – 3i)(7 + 8i) 5. (5 – 3i)2

Use the CONJUGATE The conjugate of (a + bi) is (a – bi) The conjugate of (bi) is (-bi)

Multiply both the numerator and the denominator by the complex conjugate and simplify… write the answer as a + bi

Remember: i2 = -1

1. 6 2. 3 + i 7i 3i

3. 3 + i 4. 5 – 6i 2 – i 2 – 9i