Lesson Worksheet: Quadratic Equations with Complex Coefficients Mathematics

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

Q1:

Solve (1+2𝑖)𝑧3+𝑖=0. Round your answers to three decimal places.

  • A𝑧=0.447+1.183𝑖 and 𝑧=0.4471.183𝑖
  • B𝑧=1.0680.927𝑖 and 𝑧=1.068+0.927𝑖
  • C𝑧=0.8980.779𝑖 and 𝑧=0.898+0.779𝑖
  • D𝑧=0.898+0.779𝑖 and 𝑧=0.8980.779𝑖
  • E𝑧=1.0680.927𝑖 and 𝑧=1.068+0.927𝑖

Q2:

Solve 𝑧(4+4𝑖)𝑧+8𝑖=0.

  • A𝑧=2+2𝑖
  • B2𝑖+2𝑖+1 and 2𝑖2𝑖+1
  • C𝑧=2+2𝑖+19𝑖 and 𝑧=2+2𝑖19𝑖
  • D𝑧=22𝑖
  • E𝑧=4+4𝑖

Q3:

Solve (2+3𝑖)𝑧+4𝑧6𝑖+4=0.

  • A𝑧=4+23013+633013𝑖 and 𝑧=423013+6+33013𝑖
  • B𝑧=8+32213+12+22213𝑖 and 𝑧=832213+1222213𝑖
  • C𝑧=4+32213+6+22213𝑖 and 𝑧=432213+622213𝑖
  • D𝑧=1113+1613𝑖 and 𝑧=1913413𝑖
  • E𝑧=4+32213+6+22213𝑖 and 𝑧=432213+622213𝑖

Q4:

Solve 𝑧+(22𝑖)𝑧(7+26𝑖)=0.

  • A𝑧=3+4𝑖 and 𝑧=52𝑖
  • B𝑧=6+8𝑖 and 𝑧=104𝑖
  • C𝑧=2.3063.234𝑖 and 𝑧=4.306+5.234𝑖
  • D𝑧=34𝑖 and 𝑧=5+2𝑖
  • E𝑧=3.127+4.088𝑖 and 𝑧=5.127+2.088𝑖

Q5:

Solve 𝑧+(2+𝑖)𝑧+𝑖=0.

  • A𝑧=2𝑖+23𝑖2 and 𝑧=2𝑖23𝑖2
  • B𝑧=2𝑖+3+8𝑖2 and 𝑧=2𝑖3+8𝑖2
  • C𝑧=2+32𝑖2 and 𝑧=232𝑖2
  • D𝑧=2+3𝑖 and 𝑧=23𝑖
  • E𝑧=2+32+𝑖2 and 𝑧=232+𝑖2

Q6:

Solve 3𝑧+5𝑖𝑧2=0.

  • A𝑧=5𝑖+5𝑖+246 and 𝑧=5𝑖5𝑖+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 𝑥4𝑖=0.

  • A2+2𝑖,22𝑖
  • B2𝑖,2𝑖
  • C{2𝑖,2𝑖}
  • D22𝑖
  • E2+2𝑖

Q8:

Find the solution set of the equation 𝑥5𝑖𝑥6=0 in .

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

Q9:

Solve 𝑧+6+6𝑖3𝑧+3232𝑖3=0.

  • A𝑧=3+𝑖, 𝑧=3𝑖, 𝑧=22𝑖3, 𝑧=2+2𝑖3
  • B𝑧=3+𝑖, 𝑧=3𝑖, 𝑧=22𝑖3, 𝑧=2+2𝑖3
  • C𝑧=3𝑖, 𝑧=3+𝑖, 𝑧=2+2𝑖3, 𝑧=22𝑖3
  • D𝑧=3+𝑖, 𝑧=3𝑖, 𝑧=2+2𝑖3, 𝑧=22𝑖3
  • E𝑧=3𝑖, 𝑧=3+𝑖, 𝑧=2+2𝑖3, 𝑧=22𝑖3

Q10:

Solve 3𝑧+5𝑖𝑧2=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

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