Complex Numbers

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Complex Numbers
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Complex Numbers

• The imaginary unit i is defined as

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Example
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Complex Numbers

• The set of all numbers in the form a bi with
  real numbers a and b, and i, the imaginary unit,
  is called the set of complex numbers.
• The real number a is called the real part, and
  the real number b is called the imaginary part,
  of the complex number a bi.

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Equality of Complex Numbers

• abi cdi if and only if a c and b d

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Adding and Subtracting Complex Numbers
Multiplying Complex Numbers
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Example
Simplify
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Example
Multiply
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Conjugate of a Complex Number

• The complex conjugate of the number a bi is a
  - bi, and visa-versa. The product of a complex
  number and its conjugate is a real number.

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Example
Rationalize
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Principal Square Root of a Negative Number

• For any positive real number b, the principal
  square root of the negative number -b is defined
  by

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Example
Simplify
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Quadratic Formula
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Examples
Solve