Lesson Worksheet: Dividing Complex Numbers Mathematics

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:

Put 12𝑖(1+𝑖) in the form 𝑥+𝑦𝑖.

Q10:

Simplify 19𝑖+5𝑖7𝑖6+4𝑖4𝑖+2𝑖.

  • A12𝑖
  • B1+2𝑖
  • C1+𝑖
  • D1𝑖

This lesson includes 42 additional questions and 370 additional question variations for subscribers.

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