Connections - Unit H - Complex Numbers

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Presentation transcript:

Connections - Unit H - Complex Numbers Friday, April 8 Complex Numbers Define and use imaginary and complex numbers.

Complex Numbers You can see in the graph of f(x) = x2 + 1 that f has no real zeros. However, you can find solutions if you define the square root of negative numbers, which is why imaginary numbers were invented. The imaginary unit i is defined as FHS Quadratic Function

Complex Numbers A complex number is written in the form a + bi where a and b are real numbers and i is the imaginary unit. For two complex numbers to be equal both a’s and both b’s must be equal. All numbers are complex numbers. Real numbers (the numbers we normally deal with) would be those where b is equal to 0. FHS Quadratic Function

Imaginary Numbers An imaginary number is written in the form a + bi, where b is a real number ≠ 0 and a can be equal to 0 or not. Since you can factor out a -1 from any negative number and then express the square root of a negative number as an imaginary number. FHS Quadratic Function

Examples Simplify the following. Express the numbers in terms of i. FHS Quadratic Function

Examples Find the values of x and y that make each equation true FHS Quadratic Function