Lesson Worksheet: Distance and Midpoints on the Complex Plane Mathematics

In this worksheet, we will practice finding the distance and midpoint of two complex numbers in the complex plane.

Q1:

Find the midpoint of 3+5𝑖 and 713𝑖.

  • A4+5𝑖
  • B2+9𝑖
  • C2+9𝑖
  • D54𝑖
  • E108𝑖

Q2:

What is the general form for the midpoint of two complex numbers 𝑧 and 𝑧?

  • A𝑧+𝑧2
  • B𝑧𝑧2
  • C𝑧+𝑧2
  • D2(𝑧𝑧)
  • E𝑧𝑧2

Q3:

A complex number 𝑤 lies at a distance of 52 from 𝑧=3+5𝑖 and at a distance of 45 from 𝑧=62𝑖. Is the triangle formed by the points 𝑤, 𝑧, and 𝑧 a right triangle?

  • AYes
  • BNo

Q4:

What complex number lies at the midpoint of the complex numbers 𝑟=5+3𝑖 and 𝑠=3+7𝑖 when they are represented on a complex plane?

  • A2+4𝑖
  • B1+2𝑖
  • C8+10𝑖
  • D4+5𝑖
  • E2+𝑖

Q5:

Find the complex number 𝑧 such that 4+3𝑖 lies at the midpoint of 𝑧 and 34𝑖 when they are represented on a complex plane.

  • A11+2𝑖
  • B5+10𝑖
  • C5+13𝑖
  • D1+7𝑖
  • E7𝑖

Q6:

Find the possible real values of 𝑏 such that the distance between the complex number 6+7𝑖 and the complex number 3+𝑏𝑖 is 5.

  • A3 or 11
  • B1.7 or 15.7
  • C5
  • D5 or 9
  • E0.5 or 14.5

Q7:

What complex number lies at the midpoint of the complex numbers 𝑎+𝑏𝑖 and 𝑥+𝑦𝑖, where 𝑎, 𝑏, 𝑥, and 𝑦 are real, when they are represented on a complex plane?

  • A𝑏𝑦2+𝑎𝑥2𝑖
  • B𝑎+𝑥2+𝑏+𝑦2𝑖
  • C𝑎𝑥2+𝑏𝑦2𝑖
  • D(𝑎𝑥)+(𝑏𝑦)𝑖
  • E(𝑎+𝑥)+(𝑏+𝑦)𝑖

Q8:

What is the distance between the complex numbers 𝑎+𝑏𝑖 and 𝑥+𝑦𝑖, where 𝑎,𝑏,𝑥, and 𝑦 are real?

  • A(𝑎𝑥)+(𝑏𝑦)
  • B(𝑎𝑥)+(𝑏𝑦)
  • C(𝑎𝑥)+(𝑏𝑦)
  • D(𝑎+𝑥)+(𝑏+𝑦)
  • E(𝑎+𝑥)+(𝑏+𝑦)

Q9:

What is the distance between the numbers 2𝑖 and 2+𝑖 on the complex plane?

Q10:

What is the distance between the numbers 2+3𝑖 and 2+6𝑖 on the complex plane?

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.