Lesson Worksheet: Quadratic Equations with Complex Coefficients Mathematics

Start Practising

In this worksheet, we will practice solving quadratic equations with complex coefficients using the quadratic formula.

Q1:

Solve (1+2𝑖)𝑧−3+𝑖=0. Round your answers to three decimal places.

  • A𝑧=0.447+1.183𝑖 and 𝑧=0.447−1.183𝑖
  • B𝑧=1.068−0.927𝑖 and 𝑧=−1.068+0.927𝑖
  • C𝑧=0.898−0.779𝑖 and 𝑧=−0.898+0.779𝑖
  • D𝑧=0.898+0.779𝑖 and 𝑧=0.898−0.779𝑖
  • E𝑧=1.068−0.927𝑖 and 𝑧=1.068+0.927𝑖

Q2:

Solve 𝑧−(4+4𝑖)𝑧+8𝑖=0.

  • A𝑧=2+2𝑖
  • B2𝑖+2√𝑖+1 and 2𝑖−2√𝑖+1
  • C𝑧=2+2𝑖+√−1−9𝑖 and 𝑧=2+2𝑖−√−1−9𝑖
  • D𝑧=−2−2𝑖
  • E𝑧=4+4𝑖

Q3:

Solve (2+3𝑖)𝑧+4𝑧−6𝑖+4=0.

  • A𝑧=−4+2√3013+6−3√3013𝑖 and 𝑧=−4−2√3013+6+3√3013𝑖
  • B𝑧=−8+3√2213+12+2√2213𝑖 and 𝑧=−8−3√2213+12−2√2213𝑖
  • C𝑧=−4+3√2213+6+2√2213𝑖 and 𝑧=−4−3√2213+6−2√2213𝑖
  • D𝑧=1113+1613𝑖 and 𝑧=1913−413𝑖
  • E𝑧=4+3√2213+−6+2√2213𝑖 and 𝑧=4−3√2213+−6−2√2213𝑖

Q4:

Solve 𝑧+(2−2𝑖)𝑧−(7+26𝑖)=0.

  • A𝑧=3+4𝑖 and 𝑧=−5−2𝑖
  • B𝑧=6+8𝑖 and 𝑧=−10−4𝑖
  • C𝑧=2.306−3.234𝑖 and 𝑧=−4.306+5.234𝑖
  • D𝑧=−3−4𝑖 and 𝑧=5+2𝑖
  • E𝑧=3.127+4.088𝑖 and 𝑧=−5.127+2.088𝑖

Q5:

Solve 𝑧+(2+𝑖)𝑧+𝑖=0.

  • A𝑧=−2−𝑖+√2−3𝑖2 and 𝑧=−2−𝑖−√2−3𝑖2
  • B𝑧=−2−𝑖+√3+8𝑖2 and 𝑧=−2−𝑖−√3+8𝑖2
  • C𝑧=−2+√32−𝑖2 and 𝑧=−2−√32−𝑖2
  • D𝑧=−2+√3−𝑖 and 𝑧=−2−√3−𝑖
  • E𝑧=2+√32+𝑖2 and 𝑧=2−√32+𝑖2

Q6:

Solve 3𝑧+5𝑖𝑧−2=0.

  • A𝑧=−5𝑖+√5𝑖+246 and 𝑧=−5𝑖−√5𝑖+246
  • B𝑧=−23𝑖 and 𝑧=−𝑖
  • C𝑧=𝑖3 and 𝑧=−2𝑖
  • D𝑧=23𝑖 and 𝑧=𝑖
  • E𝑧=43𝑖 and 𝑧=2𝑖

Q7:

Find the solution set of the equation 𝑥−4𝑖=0.

  • A√2+√2𝑖,−√2−√2𝑖
  • B√2𝑖,−√2𝑖
  • C{−2𝑖,2𝑖}
  • D−√2−√2𝑖
  • E√2+√2𝑖

Q8:

Find the solution set of the equation 𝑥−5𝑖𝑥−6=0 in ℂ.

  • A{2𝑖,3𝑖}
  • B{−2,−3}
  • C{−2𝑖,−3𝑖}
  • D{𝑖,6𝑖}
  • E{2,3}

Q9:

Solve 𝑧+6+6𝑖√3𝑧+32−32𝑖√3=0.

  • A𝑧=−√3+𝑖, 𝑧=√3−𝑖, 𝑧=−2−2𝑖√3, 𝑧=2+2𝑖√3
  • B𝑧=√3+𝑖, 𝑧=−√3−𝑖, 𝑧=2−2𝑖√3, 𝑧=−2+2𝑖√3
  • C𝑧=√3−𝑖, 𝑧=−√3+𝑖, 𝑧=2+2𝑖√3, 𝑧=−2−2𝑖√3
  • D𝑧=−√3+𝑖, 𝑧=√3−𝑖, 𝑧=2+2𝑖√3, 𝑧=−2−2𝑖√3
  • E𝑧=−√3−𝑖, 𝑧=√3+𝑖, 𝑧=2+2𝑖√3, 𝑧=2−2𝑖√3

Q10:

Solve 3𝑧+5𝑖𝑧−2=0.

  • A𝑧=−23 and 𝑧=−1
  • B𝑧=−23𝑖 and 𝑧=𝑖
  • C𝑧=23 and 𝑧=1
  • D𝑧=−23𝑖 and 𝑧=−𝑖
  • E𝑧=23𝑖 and 𝑧=𝑖

Practice Means Progress

Download the Nagwa Practice app to access questions, unit-exams, and flashcards for your school courses.

scan me!

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