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Products and Quotients of Complex Numbers quiz

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  • How do you multiply two complex numbers in polar form?
    Multiply their r values and add their angles.
  • What is the shortcut notation for writing a complex number in polar form?
    The shortcut is 'cis', so r cis θ stands for r(cos θ + i sin θ).
  • When multiplying complex numbers in polar form, what do you do with the angles?
    You add the angles together.
  • How do you divide two complex numbers in polar form?
    Divide their r values and subtract their angles.
  • What does 'cis θ' represent in polar form?
    'cis θ' stands for cos θ plus i times sin θ.
  • If you multiply 3 cis 15° and 2 cis 30°, what is the result?
    The result is 6 cis 45°.
  • If you divide 6 cis 45° by 3 cis 15°, what is the result?
    The result is 2 cis 30°.
  • What operation do you perform on the r values when dividing complex numbers in polar form?
    You divide the r values.
  • What operation do you perform on the angles when dividing complex numbers in polar form?
    You subtract the angles.
  • How would you write 4(cos(π/6) + i sin(π/6)) in shortcut notation?
    You would write it as 4 cis π/6.
  • What is the product of 4 cis (π/6) and 5 cis (π/3)?
    The product is 20 cis (π/2).
  • What is the quotient of 5 cis (π/3) divided by 4 cis (π/9)?
    The quotient is (5/4) cis (2π/9).
  • Why is using 'cis' notation helpful when working with complex numbers in polar form?
    It makes writing and simplifying expressions quicker and less tedious.
  • What is the general formula for multiplying two complex numbers in polar form?
    The formula is r₁ cis θ₁ times r₂ cis θ₂ equals (r₁r₂) cis (θ₁ + θ₂).
  • What is the general formula for dividing two complex numbers in polar form?
    The formula is r₁ cis θ₁ divided by r₂ cis θ₂ equals (r₁/r₂) cis (θ₁ - θ₂).