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How Do You Subtract Complex Numbers?

Subtract 3 + 4i from 7 + 9i

Summary

  1. Subtracting complex numbers is just like subtracting polynomials
  2. 'i' represents the imaginary unit and is NOT a variable
  3. The first step is to distribute the minus sign into the parentheses
  4. The real parts of the complex numbers, 7 and -3, are like terms
  5. The imaginary parts, 9i and -4i, are like terms as well
  6. We can group like terms together using the Associative Property
  7. 'i' is equal to the square root of -1
  8. We can subtract '9i-4i' just like we would '9x-4x'

Notes

    1. The minus sign needs to be distributed into the second set of parentheses
    2. Note that 'i' represents the imaginary unit and is NOT a variable here
    3. Distributing the minus sign to a positive '3' will give you '-3'
    4. Distributing the minus sign to a positive '4i' will give you '-4i'
    1. 7 and -3 are both just real numbers by themselves, so they are like terms
    2. 9i and -4i both have a number multiplied by 'i', so they are like terms
    3. Remember, 'i' is not a variable, but terms that contain 'i' are considered like terms as well
    1. Grouping the like terms together will make it easier to combine them in the next step
    2. 7 and -3 are like terms
    3. Make sure to keep the sign of each term with it when you move it!
    4. 9i and -4i are also like terms
    1. 7 and -3 are like terms, and so are 9i and -4i
    2. 7-3 = 4
    3. 9i-4i = 5i
    4. Remember, 'i' is the imaginary unit and is equal to the square root of -1
    5. Even though 'i' is not a variable, we can subtract terms with 'i's just like we do terms with variables
    6. So subtracting complex numbers is just like subtracting polynomials!