Worksheet: Quadratic Equations with Complex Coefficients

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

Q1:

Find the solution set of the equation (1𝑖)𝑥(84𝑖)𝑥+5+7𝑖=0 in .

  • A { 4 + 3 𝑖 , 2 + 3 𝑖 }
  • B { 6 + 4 𝑖 , 2 𝑖 }
  • C { 1 + 6 𝑖 , 1 }
  • D { 3 + 4 𝑖 , 3 2 𝑖 }
  • E { 6 + 𝑖 , 𝑖 }

Q2:

Find the solution set of the equation (1+𝑖)𝑥(6+2𝑖)𝑥+35𝑖=0 in .

  • A { 1 + 2 𝑖 , 3 + 2 𝑖 }
  • B { 4 + 𝑖 , 3 𝑖 }
  • C { 1 + 4 𝑖 , 1 }
  • D { 2 + 𝑖 , 2 3 𝑖 }
  • E { 4 𝑖 , 𝑖 }

Q3:

Find the solution set of the equation (1𝑖)𝑥(62𝑖)𝑥+7+𝑖=0 in .

  • A { 1 + 2 𝑖 , 3 + 2 𝑖 }
  • B { 4 + 𝑖 , 3 𝑖 }
  • C { 1 + 4 𝑖 , 1 }
  • D { 2 + 𝑖 , 2 3 𝑖 }
  • E { 1 + 2 𝑖 , 1 𝑖 }

Q4:

Find the solution set of the equation (1𝑖)𝑥(62𝑖)𝑥+6+2𝑖=0 in .

  • A { 2 + 2 𝑖 , 2 𝑖 }
  • B { 3 + 2 𝑖 , 1 }
  • C { 1 + 3 𝑖 , 1 + 𝑖 }
  • D { 2 + 2 𝑖 , 2 }
  • E { 3 + 𝑖 , 1 + 𝑖 }

Q5:

Find the solution set of the equation (1𝑖)𝑥(62𝑖)𝑥+3+5𝑖=0 in .

  • A { 3 + 2 𝑖 , 1 + 2 𝑖 }
  • B { 4 + 3 𝑖 , 𝑖 }
  • C { 1 + 4 𝑖 , 1 }
  • D { 2 + 3 𝑖 , 2 𝑖 }
  • E { 4 + 𝑖 , 𝑖 }

Q6:

Find the solution set of the equation (1+𝑖)𝑥(6+2𝑖)𝑥+7𝑖=0 in .

  • A { 1 + 2 𝑖 , 3 + 2 𝑖 }
  • B { 4 + 𝑖 , 3 𝑖 }
  • C { 1 + 4 𝑖 , 1 }
  • D { 2 + 𝑖 , 2 3 𝑖 }
  • E { 4 𝑖 , 𝑖 }

Q7:

Find the solution set of the equation (1+𝑖)𝑥(6+2𝑖)𝑥+62𝑖=0 in .

  • A { 2 𝑖 , 2 + 2 𝑖 }
  • B { 3 , 1 2 𝑖 }
  • C { 1 + 3 𝑖 , 1 + 𝑖 }
  • D { 2 , 2 2 𝑖 }
  • E { 3 𝑖 , 1 𝑖 }

Q8:

Solve 𝑧+(2+𝑖)𝑧+𝑖=0.

  • A 𝑧 = 2 𝑖 + 2 3 𝑖 2 and 𝑧=2𝑖23𝑖2
  • B 𝑧 = 2 𝑖 + 3 + 8 𝑖 2 and 𝑧=2𝑖3+8𝑖2
  • C 𝑧 = 2 + 3 2 𝑖 2 and 𝑧=232𝑖2
  • D 𝑧 = 2 + 3 𝑖 and 𝑧=23𝑖
  • E 𝑧 = 2 + 3 2 + 𝑖 2 and 𝑧=232+𝑖2

Q9:

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

  • A 𝑧 = 0 . 4 4 7 + 1 . 1 8 3 𝑖 and 𝑧=0.4471.183𝑖
  • B 𝑧 = 1 . 0 6 8 0 . 9 2 7 𝑖 and 𝑧=1.068+0.927𝑖
  • C 𝑧 = 0 . 8 9 8 0 . 7 7 9 𝑖 and 𝑧=0.898+0.779𝑖
  • D 𝑧 = 0 . 8 9 8 + 0 . 7 7 9 𝑖 and 𝑧=0.8980.779𝑖
  • E 𝑧 = 1 . 0 6 8 0 . 9 2 7 𝑖 and 𝑧=1.068+0.927𝑖

Q10:

Solve 𝑧+(22𝑖)𝑧(7+26𝑖)=0.

  • A 𝑧 = 3 + 4 𝑖 and 𝑧=52𝑖
  • B 𝑧 = 6 + 8 𝑖 and 𝑧=104𝑖
  • C 𝑧 = 2 . 3 0 6 3 . 2 3 4 𝑖 and 𝑧=4.306+5.234𝑖
  • D 𝑧 = 3 4 𝑖 and 𝑧=5+2𝑖
  • E 𝑧 = 3 . 1 2 7 + 4 . 0 8 8 𝑖 and 𝑧=5.127+2.088𝑖

Q11:

Find the solution set of the equation 𝑥4𝑖=0.

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

Q12:

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

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

Q13:

Solve 3𝑧+5𝑖𝑧2=0.

  • A 𝑧 = 5 𝑖 + 5 𝑖 + 2 4 6 and 𝑧=5𝑖5𝑖+246
  • B 𝑧 = 2 3 𝑖 and 𝑧=𝑖
  • C 𝑧 = 𝑖 3 and 𝑧=2𝑖
  • D 𝑧 = 2 3 𝑖 and 𝑧=𝑖
  • E 𝑧 = 4 3 𝑖 and 𝑧=2𝑖

Q14:

Solve (2+3𝑖)𝑧+4𝑧6𝑖+4=0.

  • A 𝑧 = 4 + 2 3 0 1 3 + 6 3 3 0 1 3 𝑖 and 𝑧=423013+6+33013𝑖
  • B 𝑧 = 8 + 3 2 2 1 3 + 1 2 + 2 2 2 1 3 𝑖 and 𝑧=832213+1222213𝑖
  • C 𝑧 = 4 + 3 2 2 1 3 + 6 + 2 2 2 1 3 𝑖 and 𝑧=432213+622213𝑖
  • D 𝑧 = 1 1 1 3 + 1 6 1 3 𝑖 and 𝑧=1913413𝑖
  • E 𝑧 = 4 + 3 2 2 1 3 + 6 + 2 2 2 1 3 𝑖 and 𝑧=432213+622213𝑖

Q15:

Solve 𝑧(4+4𝑖)𝑧+8𝑖=0.

  • A 𝑧 = 2 + 2 𝑖
  • B 2 𝑖 + 2 𝑖 + 1 and 2𝑖2𝑖+1
  • C 𝑧 = 2 + 2 𝑖 + 1 9 𝑖 and 𝑧=2+2𝑖19𝑖
  • D 𝑧 = 2 2 𝑖
  • E 𝑧 = 4 + 4 𝑖

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