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Adding, subtracting and multiplying complex numbers worksheets Grade 10

Combine real and imaginary parts and multiply complex numbers, writing a + bi.

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Free · Worked example · 21 problems · Answer key · US Letter

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How to do it

Combine the real parts and the i parts. Multiply like binomials, then replace i² with −1. Write the answer as a + bi.

(−5+6i)+(−1+7i)=(−5+(−1))+(6+7)i=−6+13i(-5 + 6i) + (-1 + 7i) = (-5 + (-1)) + (6 + 7)i = -6 + 13ireal parts together, i parts together

Example problems

  1. (3−5i)(3+5i)=(3 - 5i)(3 + 5i) =
  2. (−6+5i)(−6−5i)=(-6 + 5i)(-6 - 5i) =
  3. (2−5i)(−8−2i)=(2 - 5i)(-8 - 2i) =
  4. (−3+8i)(6+6i)=(-3 + 8i)(6 + 6i) =

Exponents, radicals and complex numbers

  1. Zero and negative exponents
  2. Rational exponents
  3. Converting between radicals and rational exponents
  4. Exponent rules with rational exponents
  5. Simplifying cube roots and higher roots
  6. Rationalizing the denominator
  7. Solving radical equations
  8. Imaginary numbers and powers of i
  9. Adding, subtracting and multiplying complex numbers
  10. Dividing complex numbers