Worksheet: Quadratic Equations with Complex Coefficients

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

Q1:

Find the solution set of the equation (1−𝑖)𝑥−(8−4𝑖)𝑥+5+7𝑖=0 in ℂ.

  • 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+3−5𝑖=0 in ℂ.

  • 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 (1−𝑖)𝑥−(6−2𝑖)𝑥+7+𝑖=0 in ℂ.

  • 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 (1−𝑖)𝑥−(6−2𝑖)𝑥+6+2𝑖=0 in ℂ.

  • 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 (1−𝑖)𝑥−(6−2𝑖)𝑥+3+5𝑖=0 in ℂ.

  • 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+7−𝑖=0 in ℂ.

  • 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+6−2𝑖=0 in ℂ.

  • 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=−2−𝑖−√2−3𝑖2
  • B 𝑧 = − 2 − 𝑖 + √ 3 + 8 𝑖 2 and 𝑧=−2−𝑖−√3+8𝑖2
  • C 𝑧 = − 2 + √ 3 2 − 𝑖 2 and 𝑧=−2−√32−𝑖2
  • D 𝑧 = − 2 + √ 3 − 𝑖 and 𝑧=−2−√3−𝑖
  • E 𝑧 = 2 + √ 3 2 + 𝑖 2 and 𝑧=2−√32+𝑖2

Q9:

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

  • A 𝑧 = 0 . 4 4 7 + 1 . 1 8 3 𝑖 and 𝑧=0.447−1.183𝑖
  • 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=0.898−0.779𝑖
  • E 𝑧 = 1 . 0 6 8 − 0 . 9 2 7 𝑖 and 𝑧=1.068+0.927𝑖

Q10:

Solve 𝑧+(2−2𝑖)𝑧−(7+26𝑖)=0.

  • A 𝑧 = 3 + 4 𝑖 and 𝑧=−5−2𝑖
  • B 𝑧 = 6 + 8 𝑖 and 𝑧=−10−4𝑖
  • 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 𝑥−4𝑖=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 𝑥−5𝑖𝑥−6=0 in ℂ.

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

Q13:

Solve 3𝑧+5𝑖𝑧−2=0.

  • A 𝑧 = − 5 𝑖 + √ 5 𝑖 + 2 4 6 and 𝑧=−5𝑖−√5𝑖+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+4𝑧−6𝑖+4=0.

  • A 𝑧 = − 4 + 2 √ 3 0 1 3 + 6 − 3 √ 3 0 1 3 𝑖 and 𝑧=−4−2√3013+6+3√3013𝑖
  • B 𝑧 = − 8 + 3 √ 2 2 1 3 + 1 2 + 2 √ 2 2 1 3 𝑖 and 𝑧=−8−3√2213+12−2√2213𝑖
  • C 𝑧 = − 4 + 3 √ 2 2 1 3 + 6 + 2 √ 2 2 1 3 𝑖 and 𝑧=−4−3√2213+6−2√2213𝑖
  • D 𝑧 = 1 1 1 3 + 1 6 1 3 𝑖 and 𝑧=1913−413𝑖
  • E 𝑧 = 4 + 3 √ 2 2 1 3 + − 6 + 2 √ 2 2 1 3 𝑖 and 𝑧=4−3√2213+−6−2√2213𝑖

Q15:

Solve 𝑧−(4+4𝑖)𝑧+8𝑖=0.

  • A 𝑧 = 2 + 2 𝑖
  • B 2 𝑖 + 2 √ 𝑖 + 1 and 2𝑖−2√𝑖+1
  • C 𝑧 = 2 + 2 𝑖 + √ − 1 − 9 𝑖 and 𝑧=2+2𝑖−√−1−9𝑖
  • D 𝑧 = − 2 − 2 𝑖
  • E 𝑧 = 4 + 4 𝑖

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