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1.3 Complex Number System
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Complex NumbersNumbers 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
1. Change (– ) to (+) of the opposite
2. Apply the Distributive Property3. Combine all like terms4. 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
1. FOIL Method for multiplying binomials
2. Distributive Property for all other polynomials
3. Follow your rules of exponents4. Combine all like terms5. 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
1. You cannot have an i in the denominator
2. Multiply numerator and denominator by the conjugate of the denominator
3. FOIL Method for multiplying binomials
4. Follow your rules of exponents5. Combine all like terms6. 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