3.3: Complex Numbers Objectives: • Define “complex” numbers

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Presentation transcript:

3.3: Complex Numbers Objectives: • Define “complex” numbers • Perform operations with complex numbers.

Concept: Solution to Quadratics RECALL: A solution to a system of of equation is the point where the two equations intersect. A solution to a quadratic or any other function is the point(s) where the graph of the equation crosses the x –axix. These are also known as roots, and x-intercepts.

Concept: Solution to Quadratics An imaginary number occurs when the graph of a quadratic function does not cross the x–axis. There is NO REAL SOLUTION.

Concept: Powers of i cont. . . Whenever the exponent is greater than 4, you can use the fact that i4 = 1 to find the value.

Concept: Powers of i cont. . . 1. Divide the exponent by 4: Rewrite I using the remainder as the exponent. Solve. Use your chart from these notes.

You Try: 5i – 7 + 2i – 8i Solution: –i – 7

Concept: Multiplying Complex Numbers Ex: (3i + 2)(5i – 6) 5i – 6 Use the box method to multiply binomials. 3i 2 15i2 –18i 10i –12 2. Write the equation. 15i2 –18i + 10i – 12 15i2 – 8i – 12 15(–1) – 8i – 12 3. Replace i2 with –1 –15 – 8i – 12 4. Simplify if possible. – 8i – 27