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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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**it is a symbol for a specific number**

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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**Simplify each expression.**

Remember 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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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. F O I L

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Simplify. F O I L

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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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Multiply Simplify Write the expression as a complex number.

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