Lesson Worksheet: Dividing Complex Numbers Mathematics • 12th Grade

In this worksheet, we will practice performing division on complex numbers.

Q1:

Given 𝑧=5+3𝑖, express 𝑧2 in the form 𝑎+𝑏𝑖.

  • A10+6𝑖
  • B52+32𝑖
  • C5+32𝑖
  • D32+52𝑖
  • E52+3𝑖

Q2:

Simplify 2+4𝑖𝑖.

  • A2+4𝑖
  • B42𝑖
  • C4+2𝑖
  • D4+2𝑖
  • E24𝑖

Q3:

Simplify 36𝑖15𝑖.

  • A3326+926𝑖
  • B913526𝑖
  • C11838𝑖
  • D34+524𝑖
  • E3+65𝑖

Q4:

Expand and simplify (𝑝+𝑞𝑖)(𝑝𝑞𝑖).

  • A𝑞𝑝
  • B𝑝+𝑞
  • C(𝑝+𝑞)
  • D𝑝𝑞
  • E(𝑝𝑞)

Expand (𝑎+𝑏𝑖)(𝑝𝑞𝑖).

  • A(𝑎𝑝𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖
  • B(𝑎𝑝𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖
  • C(𝑎𝑞+𝑏𝑝)+(𝑏𝑞𝑎𝑝)𝑖
  • D(𝑎𝑝+𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖
  • E(𝑎𝑝+𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖

Hence, find a fraction which is equivalent to 𝑎+𝑏𝑖𝑝+𝑞𝑖 and whose denominator is real.

  • A(𝑎𝑝+𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖𝑝𝑞
  • B(𝑎𝑝+𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖𝑝+𝑞
  • C(𝑎𝑝+𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖𝑝𝑞
  • D(𝑎𝑝+𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖𝑝+𝑞
  • E(𝑎𝑞+𝑏𝑝)+(𝑏𝑞𝑎𝑝)𝑖𝑝+𝑞

Q5:

If 𝑎+𝑏𝑖=35𝑖3+5𝑖, is it true that 𝑎+𝑏=1?

  • AYes
  • BNo

Q6:

Solve the equation 𝑧(2+𝑖)=3𝑖 for 𝑧.

  • A𝑧=1+𝑖2
  • B𝑧=1𝑖2
  • C𝑧=1𝑖
  • D𝑧=1+𝑖
  • E𝑧=32𝑖

Q7:

Simplify (3+2𝑖)(3+3𝑖)(4+𝑖)(4+4𝑖).

  • A15343368𝑖
  • B15343368𝑖
  • C1534+3368𝑖
  • D1534+3368𝑖

Q8:

Simplify 34𝑖2+2𝑖+34𝑖22𝑖.

  • A324𝑖
  • B322𝑖
  • C3232𝑖
  • D32+4𝑖
  • E1272𝑖

Q9:

Simplify 19𝑖+5𝑖7𝑖6+4𝑖4𝑖+2𝑖.

  • A12𝑖
  • B1+2𝑖
  • C1+𝑖
  • D1𝑖

Q10:

Given that 𝑥+𝑖𝑦13𝑖9𝑥𝑖𝑦1+3𝑖=6+5𝑖48𝑖, where 𝑥 and 𝑦 are real numbers, determine the value of 𝑥 and the value of 𝑦.

  • A𝑥=12, 𝑦=14
  • B𝑥=14, 𝑦=12
  • C𝑥=14, 𝑦=1
  • D𝑥=1, 𝑦=14

Practice Means Progress

Boost your grades with free daily practice questions. Download Nagwa Practice today!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.