Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form (8.5.3)

Question 1

• To multiply two complex numbers:
  
  • Start by putting the complex numbers in polar form.
  • Multiply the r-terms and add the θ-terms: z1z2 = r1r2[cos(theta1 + theta2) + isin(theta1 + theta2).

Answer 1

• To multiply two complex numbers:
  
  • Start by putting the complex numbers in polar form.
  • Multiply the r-terms and add the θ-terms: z1z2 = r1r2[cos(theta1 + theta2) + isin(theta1 + theta2).

Question 2

• Divide the r-terms and subtract the θ-terms: z1/z2 = r1/r2[cos(theta1 - theta2) + isin(theta1 - theta2).

Answer 2

• Divide the r-terms and subtract the θ-terms: z1/z2 = r1/r2[cos(theta1 - theta2) + isin(theta1 - theta2).