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What are complex numbers?

question
A complex number can be written in the form a + bi where a and b are real numbers (including 0) and i is the imaginary number i.
Therefore a complex number contains two 'parts';
  • one that is real
  • and another part that is imaginary.
  • Examples of a complex number
    • $$ 3 + 5 i $$
    • $$ 12 + \sqrt{-3} $$ ($$\sqrt{-3} $$ is the imaginary part)
    • $$ 4 +22i$$
    • $$ 11 - i $$
    • $$ 12 - \sqrt{-125} $$ ($$\sqrt{-125} $$ is the imaginary part)

    How do you graph complex numbers?

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    Practice Problems


    Problem 1 Identify the coordinates of all complex numbers represented in the graph below.
    Identify Complex Numbers on Graph


    Show Coordinates


    Problem 2) In what quadrant, is the complex number $$ 2- i $$ ?
    Answer


    Problem 3) In what quadrant, is the complex number $$2i -1 $$ ?
    Answer


    Problem 4) In what quadrant, is the complex number $$-i -1 $$ ?
    Answer
    Complex Number
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