Lesson Worksheet: Argand Diagram Mathematics • 12th Grade

In this worksheet, we will practice identifying complex numbers plotted on an Argand diagram and discovering their geometric properties.

Q1:

If the number 𝑍=8+𝑖 is represented on Argand diagram by the point 𝐴, determine the Cartesian coordinates of that point.

  • A(βˆ’8,1)
  • B(βˆ’8,βˆ’1)
  • C(8,βˆ’1)
  • D(8,1)

Q2:

Seven complex numbers π‘§οŠ§, π‘§οŠ¨, π‘§οŠ©, 𝑧οŠͺ, π‘§οŠ«, π‘§οŠ¬, and π‘§οŠ­ are represented on the Argand diagram.

Which of the complex numbers is βˆ’3+2𝑖?

  • Aπ‘§οŠ§
  • Bπ‘§οŠ¨
  • C𝑧οŠͺ
  • Dπ‘§οŠ©
  • Eπ‘§οŠ¬

What complex number is represented by 𝑧οŠͺ?

  • Aβˆ’4+𝑖
  • B1βˆ’4𝑖
  • C4+𝑖
  • Dβˆ’4βˆ’π‘–
  • Eβˆ’1βˆ’4𝑖

Which complex number has equal real and imaginary parts?

  • Aπ‘§οŠ­
  • Bπ‘§οŠ¬
  • Cπ‘§οŠ«
  • Dπ‘§οŠ§
  • Eπ‘§οŠ¨

Which two complex numbers are a conjugate pair? What is their geometric relationship?

  • Aπ‘§οŠ¨ and π‘§οŠ¬ are a conjugate pair; they are related by a rotation about the origin of πœ‹ radians.
  • Bπ‘§οŠ¨ and π‘§οŠ« are a conjugate pair; they are related by reflection in the real axis (π‘₯-axis).
  • CNone of the complex numbers are a conjugate pair.
  • Dπ‘§οŠ§ and π‘§οŠ¨ are a conjugate pair; they are related by reflection in the imaginary axis (𝑦-axis).
  • Eπ‘§οŠ§ and π‘§οŠ¬ are a conjugate pair; they are related by reflection in the real axis (π‘₯-axis).

Q3:

What complex number lies at the midpoint of π‘§οŠ§ and π‘§οŠ¨ on the given complex plane?

  • A8+10𝑖
  • B4+5𝑖
  • C2+2𝑖
  • D5+4𝑖
  • E4+4𝑖

Q4:

Using the Argand diagram shown, find the value of 𝑖𝑧.

  • A4βˆ’3𝑖
  • Bβˆ’3βˆ’4𝑖
  • C3+4𝑖
  • D4+3𝑖
  • Eβˆ’4+3𝑖

Q5:

Using the Argand diagram shown, find the value of 𝑧+π‘§οŠ§οŠ¨.

Q6:

Three complex numbers, π‘§οŠ§, π‘§οŠ¨, and π‘§οŠ©, are represented on the Argand diagram.

Find the complex number 𝐴 that lies at the midpoint between π‘§οŠ§ and π‘§οŠ©.

  • A2βˆ’π‘–
  • Bβˆ’1+5𝑖
  • C4βˆ’π‘–
  • D4+2𝑖
  • E8βˆ’2𝑖

Find the value of 𝐴+π‘§οŠ¨.

  • Aβˆ’4+3𝑖
  • B2+𝑖
  • C6βˆ’2𝑖
  • Dβˆ’3+7𝑖
  • E2+4𝑖

Q7:

What is the geometric relationship between the points representing a conjugate pair of complex numbers on an Argand diagram?

  • AThey both lie on the imaginary axis.
  • BThey are reflections of each other in the real axis.
  • CThey are rotations of each other of πœ‹ radians counterclockwise about the origin.
  • DThey both lie on the real axis.
  • EThey are reflections of each other in the imaginary axis.

Q8:

Using the Argand diagram below, find the value of βˆ’2𝑧.

  • Aβˆ’2𝑖
  • Bβˆ’2+4𝑖
  • C2+4𝑖
  • D2βˆ’4𝑖
  • Eβˆ’2βˆ’4𝑖

Q9:

Consider the complex number 𝑧=5+3𝑖. If 𝑖𝑧 is represented on an Argand diagram by the point 𝐴, in which quadrant of the Argand plane does 𝐴 lie?

  • AFirst
  • BSecond
  • CThird
  • DFourth

Q10:

Find the value of 2𝑧+𝑖̄𝑧 given 𝑧 on the Argand diagram below.

  • A3+14𝑖
  • B13+14𝑖
  • C9+9𝑖
  • D13+6𝑖
  • E12+5𝑖

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