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How Do You Graph Complex Numbers?

Graph 5+3i, -2+7i, and 4-3i on the complex plane.

Summary

  1. The real axis is the horizontal axis
  2. The imaginary axis is the vertical axis
  3. The real part of A is positive 5, so move right 5 units on the real axis
  4. The imaginary part of A is positive 3i, so move up 3 units on the imaginary axis
  5. 'i' is the imaginary unit and is equal to the square root of -1
  6. The real part of B is negative 2, so move left 2 units on the real axis
  7. The imaginary part of B is positive 7i, so move up 7 units on the imaginary axis
  8. The real part of C is positive 4, so move right 4 units on the real axis
  9. The imaginary part of C is negative 3i, so move down 3 units on the imaginary axis

Notes

    1. The complex plane is the coordinate system we use to graph complex numbers
    2. Just like the coordinate plane, the complex plane has two axes
    3. But the horizontal axis is the real axis and the vertical axis is the imaginary axis
    4. So we graph the real part of the complex number on the real axis and the imaginary part on the imaginary axis
    1. 'i' is the imaginary unit and is equal to the square root of -1
    1. Complex numbers have a real part and an imaginary part
    2. The imaginary part is the part with the 'i'
    3. 'i' is the imaginary unit and is equal to the square root of -1
    4. 5 is the part that does NOT have an 'i', so it is the real part
    5. +3i is the part that DOES have an 'i', so it is the imaginary part
    1. We can graph complex numbers on the complex plane just like we graph ordered pairs on the coordinate plane
    2. But this time we use the real and imaginary parts of the complex number instead of x- and y-coordinates
    1. The real axis is the horizontal axis on the complex plane
    2. Just like the x-axis on the coordinate plane, we move to the right if the real part is positive and left if it is negative
    3. The imaginary axis is the vertical axis on the complex plane
    4. Just like the y-axis on the coordinate plane, we move up if the imaginary part is positive and down if it is negative
    1. 'i' is the imaginary unit and is equal to the square root of -1
    1. Complex numbers have a real part and an imaginary part
    2. The imaginary part is the part with the 'i'
    3. 'i' is the imaginary unit and is equal to the square root of -1
    4. -2 is the part that does NOT have an 'i', so it is the real part
    5. +7i is the part that DOES have an 'i', so it is the imaginary part
    1. We can graph complex numbers on the complex plane just like we graph ordered pairs on the coordinate plane
    2. But this time we use the real and imaginary parts of the complex number instead of x- and y-coordinates
    1. The real axis is the horizontal axis on the complex plane
    2. Just like the x-axis on the coordinate plane, we move to the right if the real part is positive and left if it is negative
    3. The imaginary axis is the vertical axis on the complex plane
    4. Just like the y-axis on the coordinate plane, we move up if the imaginary part is positive and down if it is negative
    1. 'i' is the imaginary unit and is equal to the square root of -1
    1. Complex numbers have a real part and an imaginary part
    2. The imaginary part is the part with the 'i'
    3. 'i' is the imaginary unit and is equal to the square root of -1
    4. 4 is the part that does NOT have an 'i', so it is the real part
    5. -3i is the part that DOES have an 'i', so it is the imaginary part
    1. We can graph complex numbers on the complex plane just like we graph ordered pairs on the coordinate plane
    2. But this time we use the real and imaginary parts of the complex number instead of x- and y-coordinates
    1. The real axis is the horizontal axis on the complex plane
    2. Just like the x-axis on the coordinate plane, we move to the right if the real part is positive and left if it is negative
    3. The imaginary axis is the vertical axis on the complex plane
    4. Just like the y-axis on the coordinate plane, we move up if the imaginary part is positive and down if it is negative