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Precalculus
9-6    Complex Plane and Polar Form of Complex Numbers

Plotting Complex Numbers
Define the complex plane:


Plot   (a) z = 3 + 2ι


       (b) z = 4 ι




Absolute Value means ____________________________________________________.

Use Pythagorean Theorem to find absolute value of a complex number:




Find the absolute values of the examples above.




Complex Numbers as Polar Coordinates
What is r? __________________________________________
    • This is also called the ____________________ of the complex number.
θ is called the _________________________ of the complex number.

Complex numbers can be written in polar form by substituting a = ρχοσθ and b = ρσ θ .
                                                                                 ιν
      Polar form of a + βι is _______________________
EX1: Solve the equation for x and y, where x and y are real numbers.
             2x + ψ+ 3ι = 9 ξι − ψι




EX2: Express the complex number in polar form.
            −3 + 4i




              1+ ι 3




HW p. 590 (16 – 34 even)

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Pc9 6 complexplane notes

  • 1. Precalculus 9-6 Complex Plane and Polar Form of Complex Numbers Plotting Complex Numbers Define the complex plane: Plot (a) z = 3 + 2ι (b) z = 4 ι Absolute Value means ____________________________________________________. Use Pythagorean Theorem to find absolute value of a complex number: Find the absolute values of the examples above. Complex Numbers as Polar Coordinates What is r? __________________________________________ • This is also called the ____________________ of the complex number. θ is called the _________________________ of the complex number. Complex numbers can be written in polar form by substituting a = ρχοσθ and b = ρσ θ . ιν Polar form of a + βι is _______________________
  • 2. EX1: Solve the equation for x and y, where x and y are real numbers. 2x + ψ+ 3ι = 9 ξι − ψι EX2: Express the complex number in polar form. −3 + 4i 1+ ι 3 HW p. 590 (16 – 34 even)