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Complex Numbers

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Definition of pure imaginary numbers: Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.

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Definition of pure imaginary numbers: i is not a variable it is a symbol for a specific number

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Simplify each expression.

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Remember Simplify each expression. Remember

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Definition of Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary unit.

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Definition of Equal Complex Numbers Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d

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When adding or subtracting complex numbers, combine like terms.

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Solving quadratic functions with complex numbers subtract 2 Take the square root of both sides simplify

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Simplify.

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Multiplying complex numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials.

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Simplify. FOIL

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FOIL

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CONJUGATES Each imaginary unit has a conjugate. Two imaginary units are conjugates if and only if their products are a real number.

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Dividing complex numbers. To divide complex numbers you must multiply the numerator and denominator by the conjugate of the denominator.

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What’s the conjugate of the denominator?

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Your turn. Write in standard form by dividing.

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Graphing complex numbers y-axis is the imaginary axis. x-axis is the real numbers Identify the numbers plotted.

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