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 (1βˆ’π‘–)π‘₯βˆ’(8βˆ’4𝑖)π‘₯+5+7𝑖=0 in β„‚.

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

Q2:

Find the solution set of the equation (1+𝑖)π‘₯βˆ’(6+2𝑖)π‘₯+3βˆ’5𝑖=0 in β„‚.

  • A{1+2𝑖,βˆ’3+2𝑖}
  • B{4+𝑖,βˆ’3𝑖}
  • C{βˆ’1+4𝑖,βˆ’1}
  • D{2+𝑖,2βˆ’3𝑖}
  • E{4βˆ’π‘–,βˆ’π‘–}

Q3:

Find the solution set of the equation (1βˆ’π‘–)π‘₯βˆ’(6βˆ’2𝑖)π‘₯+7+𝑖=0 in β„‚.

  • A{1+2𝑖,βˆ’3+2𝑖}
  • B{4+𝑖,βˆ’3𝑖}
  • C{βˆ’1+4𝑖,βˆ’1}
  • D{2+𝑖,2βˆ’3𝑖}
  • E{1+2𝑖,1βˆ’π‘–}

Q4:

Find the solution set of the equation (1βˆ’π‘–)π‘₯βˆ’(6βˆ’2𝑖)π‘₯+6+2𝑖=0 in β„‚.

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

Q5:

Find the solution set of the equation (1βˆ’π‘–)π‘₯βˆ’(6βˆ’2𝑖)π‘₯+3+5𝑖=0 in β„‚.

  • A{3+2𝑖,βˆ’1+2𝑖}
  • B{4+3𝑖,βˆ’π‘–}
  • C{1+4𝑖,1}
  • D{2+3𝑖,2βˆ’π‘–}
  • E{4+𝑖,𝑖}

Q6:

Find the solution set of the equation (1+𝑖)π‘₯βˆ’(6+2𝑖)π‘₯+7βˆ’π‘–=0 in β„‚.

  • A{1+2𝑖,βˆ’3+2𝑖}
  • B{4+𝑖,βˆ’3𝑖}
  • C{βˆ’1+4𝑖,βˆ’1}
  • D{2+𝑖,2βˆ’3𝑖}
  • E{4βˆ’π‘–,βˆ’π‘–}

Q7:

Find the solution set of the equation (1+𝑖)π‘₯βˆ’(6+2𝑖)π‘₯+6βˆ’2𝑖=0 in β„‚.

  • A{2𝑖,βˆ’2+2𝑖}
  • B{3,1βˆ’2𝑖}
  • C{βˆ’1+3𝑖,βˆ’1+𝑖}
  • D{2,2βˆ’2𝑖}
  • E{3βˆ’π‘–,1βˆ’π‘–}

Q8:

Solve 𝑧+(2+𝑖)𝑧+𝑖=0.

  • A𝑧=βˆ’2βˆ’π‘–+√2βˆ’3𝑖2 and 𝑧=βˆ’2βˆ’π‘–βˆ’βˆš2βˆ’3𝑖2
  • B𝑧=βˆ’2βˆ’π‘–+√3+8𝑖2 and 𝑧=βˆ’2βˆ’π‘–βˆ’βˆš3+8𝑖2
  • C𝑧=βˆ’2+√32βˆ’π‘–2 and 𝑧=βˆ’2βˆ’βˆš32βˆ’π‘–2
  • D𝑧=ο€»βˆ’2+√3ο‡βˆ’π‘– and 𝑧=ο€»βˆ’2βˆ’βˆš3ο‡βˆ’π‘–
  • E𝑧=2+√32+𝑖2 and 𝑧=2βˆ’βˆš32+𝑖2

Q9:

Solve (1+2𝑖)π‘§βˆ’3+𝑖=0. Round your answers to three significant figures.

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

Q10:

Solve 𝑧+(2βˆ’2𝑖)π‘§βˆ’(7+26𝑖)=0.

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

Q11:

Find the solution set of the equation π‘₯βˆ’4𝑖=0.

  • A√2+√2𝑖,βˆ’βˆš2βˆ’βˆš2𝑖
  • B√2𝑖,βˆ’βˆš2𝑖
  • C{βˆ’2𝑖,2𝑖}
  • Dο«βˆ’βˆš2βˆ’βˆš2𝑖
  • E√2+√2𝑖

Q12:

Find the solution set of the equation π‘₯βˆ’5𝑖π‘₯βˆ’6=0 in β„‚.

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

Q13:

Solve 3𝑧+5π‘–π‘§βˆ’2=0.

  • A𝑧=βˆ’5𝑖+√5𝑖+246 and 𝑧=βˆ’5π‘–βˆ’βˆš5𝑖+246
  • B𝑧=βˆ’23𝑖 and 𝑧=βˆ’π‘–
  • C𝑧=𝑖3 and 𝑧=βˆ’2𝑖
  • D𝑧=23𝑖 and 𝑧=𝑖
  • E𝑧=43𝑖 and 𝑧=2𝑖

Q14:

Solve (2+3𝑖)𝑧+4π‘§βˆ’6𝑖+4=0.

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

Q15:

Solve π‘§βˆ’(4+4𝑖)𝑧+8𝑖=0.

  • A𝑧=2+2𝑖
  • B2𝑖+2βˆšπ‘–+1 and 2ο€»π‘–βˆ’2βˆšπ‘–+1
  • C𝑧=2+2𝑖+βˆšβˆ’1βˆ’9𝑖 and 𝑧=2+2π‘–βˆ’βˆšβˆ’1βˆ’9𝑖
  • D𝑧=βˆ’2βˆ’2𝑖
  • E𝑧=4+4𝑖

Q16:

Solve 3𝑧+5π‘–π‘§βˆ’2=0.

  • A𝑧=βˆ’23 and 𝑧=βˆ’1
  • B𝑧=βˆ’23𝑖 and 𝑧=𝑖
  • C𝑧=23 and 𝑧=1
  • D𝑧=βˆ’23𝑖 and 𝑧=βˆ’π‘–
  • E𝑧=23𝑖 and 𝑧=𝑖

Q17:

Solve π‘§βˆ’(4+4𝑖)𝑧+8𝑖=0.

  • A𝑧=2+2𝑖
  • B𝑧=4+4𝑖
  • C𝑧=βˆ’2+2𝑖
  • D𝑧=2βˆ’2𝑖
  • E𝑧=βˆ’4βˆ’4𝑖

Q18:

Solve 𝑧+(2βˆ’2𝑖)π‘§βˆ’(7+26𝑖)=0.

  • A𝑧=βˆ’3+4𝑖 and 𝑧=βˆ’5βˆ’2𝑖
  • B𝑧=3βˆ’4𝑖 and 𝑧=βˆ’5+2𝑖
  • C𝑧=βˆ’3βˆ’4𝑖 and 𝑧=5+2𝑖
  • D𝑧=3+4𝑖 and 𝑧=βˆ’5βˆ’2𝑖
  • E𝑧=3+4𝑖 and 𝑧=βˆ’5+2𝑖

Q19:

Solve (1+2𝑖)π‘§βˆ’3+𝑖=0. Round your answers to three significant figures.

  • A𝑧=0.898βˆ’0.779𝑖 and 𝑧=βˆ’0.898+0.779𝑖
  • B𝑧=0.898+0.779𝑖 and 𝑧=βˆ’0.898βˆ’0.779𝑖
  • C𝑧=0.898βˆ’0.779𝑖 and 𝑧=0.898+0.779𝑖
  • D𝑧=0.779+0.898𝑖 and 𝑧=βˆ’0.779βˆ’0.898𝑖
  • E𝑧=0.779βˆ’0.898𝑖 and 𝑧=βˆ’0.779+0.898𝑖

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