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 π‘Ž+𝑏𝑖.

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

Q2:

Simplify 2+4𝑖𝑖.

  • A2+4𝑖
  • B4βˆ’2𝑖
  • C4+2𝑖
  • Dβˆ’4+2𝑖
  • Eβˆ’2βˆ’4𝑖

Q3:

Simplify 3βˆ’6𝑖1βˆ’5𝑖.

  • A3326+926𝑖
  • Bβˆ’913βˆ’526𝑖
  • Cβˆ’118βˆ’38𝑖
  • D34+524𝑖
  • E3+65𝑖

Q4:

Expand and simplify (𝑝+π‘žπ‘–)(π‘βˆ’π‘žπ‘–).

  • Aπ‘žβˆ’π‘οŠ¨οŠ¨
  • B𝑝+π‘žοŠ¨οŠ¨
  • C(𝑝+π‘ž)
  • Dπ‘βˆ’π‘žοŠ¨οŠ¨
  • E(π‘βˆ’π‘ž)

Expand (π‘Ž+𝑏𝑖)(π‘βˆ’π‘žπ‘–).

  • A(π‘Žπ‘βˆ’π‘π‘ž)+(π‘π‘βˆ’π‘Žπ‘ž)𝑖
  • B(π‘Žπ‘βˆ’π‘π‘ž)βˆ’(π‘π‘βˆ’π‘Žπ‘ž)𝑖
  • C(π‘Žπ‘ž+𝑏𝑝)+(π‘π‘žβˆ’π‘Žπ‘)𝑖
  • D(π‘Žπ‘+π‘π‘ž)+(π‘π‘βˆ’π‘Žπ‘ž)𝑖
  • E(π‘Žπ‘+π‘π‘ž)βˆ’(π‘π‘βˆ’π‘Žπ‘ž)𝑖

Hence, find a fraction which is equivalent to π‘Ž+𝑏𝑖𝑝+π‘žπ‘– and whose denominator is real.

  • A(π‘Žπ‘+π‘π‘ž)+(π‘π‘βˆ’π‘Žπ‘ž)π‘–π‘βˆ’π‘žοŠ¨οŠ¨
  • B(π‘Žπ‘+π‘π‘ž)βˆ’(π‘π‘βˆ’π‘Žπ‘ž)𝑖𝑝+π‘žοŠ¨οŠ¨
  • C(π‘Žπ‘+π‘π‘ž)βˆ’(π‘π‘βˆ’π‘Žπ‘ž)π‘–π‘βˆ’π‘žοŠ¨οŠ¨
  • D(π‘Žπ‘+π‘π‘ž)+(π‘π‘βˆ’π‘Žπ‘ž)𝑖𝑝+π‘žοŠ¨οŠ¨
  • E(π‘Žπ‘ž+𝑏𝑝)+(π‘π‘žβˆ’π‘Žπ‘)𝑖𝑝+π‘žοŠ¨οŠ¨

Q5:

If π‘Ž+𝑏𝑖=βˆ’3βˆ’5π‘–βˆ’3+5𝑖, is it true that π‘Ž+𝑏=1?

  • AYes
  • BNo

Q6:

Solve the equation 𝑧(2+𝑖)=3βˆ’π‘– for 𝑧.

  • A𝑧=1+𝑖2
  • B𝑧=1βˆ’π‘–2
  • C𝑧=1βˆ’π‘–
  • D𝑧=1+𝑖
  • E𝑧=32βˆ’π‘–

Q7:

Simplify (βˆ’3+2𝑖)(3+3𝑖)(4+𝑖)(4+4𝑖).

  • Aβˆ’1534βˆ’3368𝑖
  • B1534βˆ’3368𝑖
  • Cβˆ’1534+3368𝑖
  • D1534+3368𝑖

Q8:

Simplify 3βˆ’4𝑖2+2𝑖+3βˆ’4𝑖2βˆ’2𝑖.

  • A32βˆ’4𝑖
  • B32βˆ’2𝑖
  • C32βˆ’32𝑖
  • D32+4𝑖
  • Eβˆ’12βˆ’72𝑖

Q9:

Simplify βˆ’1βˆ’9𝑖+5π‘–βˆ’7π‘–βˆ’6+4π‘–βˆ’4𝑖+2π‘–οŠ¨οŠ©οŠ¨οŠ©.

  • A1βˆ’2𝑖
  • B1+2𝑖
  • Cβˆ’1+𝑖
  • Dβˆ’1βˆ’π‘–

Q10:

Given that π‘₯+𝑖𝑦1βˆ’3π‘–βˆ’9π‘₯βˆ’π‘–π‘¦1+3𝑖=6+5𝑖4βˆ’8𝑖, where π‘₯ and 𝑦 are real numbers, determine the value of π‘₯ and the value of 𝑦.

  • Aπ‘₯=12, 𝑦=14
  • Bπ‘₯=14, 𝑦=12
  • Cπ‘₯=14, 𝑦=1
  • Dπ‘₯=1, 𝑦=14

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