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1.3 Complex Number System

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Complex Numbers Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit.

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**Add / Subtract Complex Numbers**

Change (– ) to (+) of the opposite Apply the Distributive Property Combine all like terms Write your answer in the form of a + bi

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**Simplify each expression in standard form**

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**Multiplying Complex Numbers**

FOIL Method for multiplying binomials Distributive Property for all other polynomials Follow your rules of exponents Combine all like terms Write your answer in the form of a + bi

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**Simplify each expression in standard form**

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Conjugate

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**The conjugate of the conjugate of a complex number is the complex number itself.**

The conjugate of the sum of two complex numbers equals the sum of their conjugates. The conjugate of the product of two complex numbers equals the product of their conjugates.

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**Simplify using Conjugates**

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**Dividing Complex Numbers**

You cannot have an i in the denominator Multiply numerator and denominator by the conjugate of the denominator FOIL Method for multiplying binomials Follow your rules of exponents Combine all like terms Write your answer in the form of a + bi

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**Simplify each expression in standard form**

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Evaluate Powers of i

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Evaluate Square Roots Perform the indicated operation and express your answer in standard form

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**Perform the indicated operation and express your answer in standard form**

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**Character of Solutions**

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**Determine the character of the solutions of each quadratic equation.**

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**Solve each equation in the complex number system**

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