PreCalc 2.4 Complex Numbers. - Section 2.4 Complex Numbers Do Now Using the rational root theorem synthetic division and your graphing calculator find

PreCalc 2.4 Complex Numbers. - Section 2.4 Complex Numbers...

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Section 2.4 Complex Numbers Complex Numbers Do Now: Using the rational root theorem, synthetic division and your graphing calculator, find all real solutions of the equation: 5 4 3 2 5 6 0 x x x x x = Homework (Two Days) 15 – 51 (odd) Write a complete factor form version of the polynomial function above, using only real factors..
The Imaginary Unit i Imaginary numbers appears because our need to solve equations that other wise will have no solutions in the real number set. 1 i = Imaginary Unit 2 1 i − = Definition of a complex Number If a and b are real numbers the number a+bi is a complex number in standard form. If b = 0 then a+bi = a is a pure real number . If a = 0 then a+bi = bi is a pure imaginary number .
Operations with Complex Numbers Sum: ( ) ( ) ( ) ( ) Difference: ( ) ( ) ( ) ( ) Product: ( ) ( ) ( ) ( ) a bi c di a c b d i a bi c di a c b d i a bi c di a c di bi c di ac adi bci bdi + + + = + + + + + = + + + = + + + = + + + 2 ( ) ( ) ac bd ad bc i = + + Bottom Line: For the sum and difference just combine real parts together and imaginary parts together.

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