Warm-up 7-7

Lesson 7-7: Imaginary & Complex Numbers Objectives: Students will: Express the square root of negative numbers and their products in terms of I Add or subtract complex numbers

Imaginary Numbers Used to solve the square roots of negatives i is the imaginary unit where i2 = -1 Since i2 = -1, then Find a pattern i1 = i2 = i3 = i4 = i5 = i6 = Pattern:

Numbers with a real and imaginary parts Example 1 Example 2 Example 3 If there is a negative under a square (even) root you must factor a “-1” Complex Numbers Numbers with a real and imaginary parts a + bi ; a and b are real numbers You can add and subtract like parts

Example 4 Example 5 (2i + 1) + (5i + 3) (-4i – 3) – (2i + 5) HW 84