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Imaginary Numbers and Negative Square Roots. The imaginary number i is the square root of -1: Example: Evaluate (3 i) 2 Imaginary Numbers.

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Presentation on theme: "Imaginary Numbers and Negative Square Roots. The imaginary number i is the square root of -1: Example: Evaluate (3 i) 2 Imaginary Numbers."— Presentation transcript:

1 Imaginary Numbers and Negative Square Roots

2 The imaginary number i is the square root of -1: Example: Evaluate (3 i) 2 Imaginary Numbers

3 Generalizing Powers of i PatternExamples After 4, it starts to repeat itself! Evaluate the examples by first finding a pattern for raising i to a power: Divide the exponent by 4 and find the remainder. The remainder is where it falls in the pattern: Divide by 4 Remainder

4 Evaluating a Negative Square Root “Factor” out a -1 Rewrite Simplify Calculate the value of the expression below:

5 The Calculator and Imaginary Numbers Hit “Mode” on your calculator. Locate where the word “REAL” is highlighted. Highlight “ a + bi ” instead. Now your calculator will work with imaginary numbers. The imaginary number “ i ” is found on the calculator by pressing “2ND” and “.” Examples: Use the calculator to evaluate the following.

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