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Dividing complex numbers worksheets Grade 10

Multiply the top and bottom by the conjugate, then write a + bi.

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How to do it

Multiply the top and the bottom by the conjugate of the bottom (a + bi becomes a − bi). Write the answer as a + bi.

8−12i−4i=(8−12i)(4i)(−4i)(4i)\dfrac{8 - 12i}{-4i} = \dfrac{(8 - 12i)(4i)}{(-4i)(4i)}multiply the top and the bottom by the conjugate, 4i
(8−12i)(4i)(−4i)(4i)=32i−48i216=48+32i16=3+2i\dfrac{(8 - 12i)(4i)}{(-4i)(4i)} = \dfrac{32i - 48i^{2}}{16} = \dfrac{48 + 32i}{16} = 3 + 2ithe bottom is (−4)² = 16; divide both parts by 16

Example problems

  1. 40−13i2−5i=\dfrac{40 - 13i}{2 - 5i} =
  2. 30−25i5i=\dfrac{30 - 25i}{5i} =
  3. −8+4i2i=\dfrac{-8 + 4i}{2i} =
  4. −5−15i−5i=\dfrac{-5 - 15i}{-5i} =

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