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Imaginary numbers and powers of i worksheets Grade 10

Simplify square roots of negatives and powers of i.

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Free · Worked example · 40 problems · Answer key · US Letter

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How to do it

i = √−1 and i² = −1. Write √−n as i√n first, then simplify. The powers of i repeat: i, −1, −i, 1.

−3=−1⋅3=i3\sqrt{-3} = \sqrt{-1 \cdot 3} = i\sqrt{3}√−1 = i

Example problems

  1. i21=i^{21} =
  2. −108⋅−3=\sqrt{-108} \cdot \sqrt{-3} =
  3. i41=i^{41} =
  4. −9=\sqrt{-9} =

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