5'9 Complex Numbers 1907

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5.9 Complex Numbers1/9/07

• imaginary unit principal square root
  of -1
• Pure Imaginary Numbers square roots of negative
  real numbers

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Square Roots of Negative Numbers

• For any positive real number b,
  or bi.
• Examples Simplify.
• a.
• b.

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Multiply Pure Imaginary Numbers

• Simplify
• a.

• Simplify
• b.

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Simplify a Power of i

• Simplify .

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Equation with Imaginary Solutions

• Solve .

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Complex Numbers

• A complex number any number that can be written
  in the form a bi, where a and b are real
  numbers and i is the imaginary unit. a is also
  called the real part, and b is called the
  imaginary part.
• Ex. 7 4i and 2 6i 2 (-6)i

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Equate Complex Numbers

• Find the values of x and y that make the equation
  
• 2x 3 (y 4)i 3 2i true.
• First, set the real parts equal to each other and
  the imaginary parts equal to each other.

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Add and Subtract Complex Numbers

• To add and subtract complex numbers, combine like
  terms. That is, combine the real parts and
  combine the imaginary parts.
• Simplify.
• a.
• b.

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Multiply Complex Numbers

• You can use the FOIL method to multiply complex
• Simplify.

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Divide Complex Numbers

• Complex Conjugates numbers in the form abi and
  a bi.
• Simplify.
• a.
• - standard form

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Divide Complex Numbers

• Simplify.
• b.
• - standard form

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More Practice!!!

• Textbook p. 274 18 32 even