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+2๐‘–)๐‘งโˆ’3+๐‘–=0๏Šจ. Round your answers to three decimal places.

  • A๐‘ง=0.447+1.183๐‘– and ๐‘ง=0.447โˆ’1.183๐‘–
  • B๐‘ง=1.068โˆ’0.927๐‘– and ๐‘ง=โˆ’1.068+0.927๐‘–
  • C๐‘ง=0.898โˆ’0.779๐‘– and ๐‘ง=โˆ’0.898+0.779๐‘–
  • D๐‘ง=0.898+0.779๐‘– and ๐‘ง=0.898โˆ’0.779๐‘–
  • E๐‘ง=1.068โˆ’0.927๐‘– and ๐‘ง=1.068+0.927๐‘–

Q2:

Solve ๐‘งโˆ’(4+4๐‘–)๐‘ง+8๐‘–=0๏Šจ.

  • A๐‘ง=2+2๐‘–
  • B2๏€ป๐‘–+2โˆš๐‘–+1๏‡ and 2๏€ป๐‘–โˆ’2โˆš๐‘–+1๏‡
  • C๐‘ง=2+2๐‘–+โˆšโˆ’1โˆ’9๐‘– and ๐‘ง=2+2๐‘–โˆ’โˆšโˆ’1โˆ’9๐‘–
  • D๐‘ง=โˆ’2โˆ’2๐‘–
  • E๐‘ง=4+4๐‘–

Q3:

Solve (2+3๐‘–)๐‘ง+4๐‘งโˆ’6๐‘–+4=0๏Šจ.

  • A๐‘ง=โˆ’4+2โˆš3013+6โˆ’3โˆš3013๐‘– and ๐‘ง=โˆ’4โˆ’2โˆš3013+6+3โˆš3013๐‘–
  • B๐‘ง=โˆ’8+3โˆš2213+12+2โˆš2213๐‘– and ๐‘ง=โˆ’8โˆ’3โˆš2213+12โˆ’2โˆš2213๐‘–
  • C๐‘ง=โˆ’4+3โˆš2213+6+2โˆš2213๐‘– and ๐‘ง=โˆ’4โˆ’3โˆš2213+6โˆ’2โˆš2213๐‘–
  • D๐‘ง=1113+1613๐‘– and ๐‘ง=1913โˆ’413๐‘–
  • E๐‘ง=4+3โˆš2213+โˆ’6+2โˆš2213๐‘– and ๐‘ง=4โˆ’3โˆš2213+โˆ’6โˆ’2โˆš2213๐‘–

Q4:

Solve ๐‘ง+(2โˆ’2๐‘–)๐‘งโˆ’(7+26๐‘–)=0๏Šจ.

  • A๐‘ง=3+4๐‘– and ๐‘ง=โˆ’5โˆ’2๐‘–
  • B๐‘ง=6+8๐‘– and ๐‘ง=โˆ’10โˆ’4๐‘–
  • C๐‘ง=2.306โˆ’3.234๐‘– and ๐‘ง=โˆ’4.306+5.234๐‘–
  • D๐‘ง=โˆ’3โˆ’4๐‘– and ๐‘ง=5+2๐‘–
  • E๐‘ง=3.127+4.088๐‘– and ๐‘ง=โˆ’5.127+2.088๐‘–

Q5:

Solve ๐‘ง+(2+๐‘–)๐‘ง+๐‘–=0๏Šจ.

  • A๐‘ง=โˆ’2โˆ’๐‘–+โˆš2โˆ’3๐‘–2 and ๐‘ง=โˆ’2โˆ’๐‘–โˆ’โˆš2โˆ’3๐‘–2
  • B๐‘ง=โˆ’2โˆ’๐‘–+โˆš3+8๐‘–2 and ๐‘ง=โˆ’2โˆ’๐‘–โˆ’โˆš3+8๐‘–2
  • C๐‘ง=โˆ’2+โˆš32โˆ’๐‘–2 and ๐‘ง=โˆ’2โˆ’โˆš32โˆ’๐‘–2
  • D๐‘ง=๏€ปโˆ’2+โˆš3๏‡โˆ’๐‘– and ๐‘ง=๏€ปโˆ’2โˆ’โˆš3๏‡โˆ’๐‘–
  • E๐‘ง=2+โˆš32+๐‘–2 and ๐‘ง=2โˆ’โˆš32+๐‘–2

Q6:

Solve 3๐‘ง+5๐‘–๐‘งโˆ’2=0๏Šจ.

  • A๐‘ง=โˆ’5๐‘–+โˆš5๐‘–+246 and ๐‘ง=โˆ’5๐‘–โˆ’โˆš5๐‘–+246
  • B๐‘ง=โˆ’23๐‘– and ๐‘ง=โˆ’๐‘–
  • C๐‘ง=๐‘–3 and ๐‘ง=โˆ’2๐‘–
  • D๐‘ง=23๐‘– and ๐‘ง=๐‘–
  • E๐‘ง=43๐‘– and ๐‘ง=2๐‘–

Q7:

Find the solution set of the equation ๐‘ฅโˆ’4๐‘–=0๏Šจ.

  • A๏ซโˆš2+โˆš2๐‘–,โˆ’โˆš2โˆ’โˆš2๐‘–๏ท
  • B๏ซโˆš2๐‘–,โˆ’โˆš2๐‘–๏ท
  • C{โˆ’2๐‘–,2๐‘–}
  • D๏ซโˆ’โˆš2โˆ’โˆš2๐‘–๏ท
  • E๏ซโˆš2+โˆš2๐‘–๏ท

Q8:

Find the solution set of the equation ๐‘ฅโˆ’5๐‘–๐‘ฅโˆ’6=0๏Šจ in โ„‚.

  • A{2๐‘–,3๐‘–}
  • B{โˆ’2,โˆ’3}
  • C{โˆ’2๐‘–,โˆ’3๐‘–}
  • D{๐‘–,6๐‘–}
  • E{2,3}

Q9:

Solve ๐‘ง+๏€ป6+6๐‘–โˆš3๏‡๐‘ง+32โˆ’32๐‘–โˆš3=0๏Šช๏Šจ.

  • A๐‘ง=โˆ’โˆš3+๐‘–, ๐‘ง=โˆš3โˆ’๐‘–, ๐‘ง=โˆ’2โˆ’2๐‘–โˆš3, ๐‘ง=2+2๐‘–โˆš3
  • B๐‘ง=โˆš3+๐‘–, ๐‘ง=โˆ’โˆš3โˆ’๐‘–, ๐‘ง=2โˆ’2๐‘–โˆš3, ๐‘ง=โˆ’2+2๐‘–โˆš3
  • C๐‘ง=โˆš3โˆ’๐‘–, ๐‘ง=โˆ’โˆš3+๐‘–, ๐‘ง=2+2๐‘–โˆš3, ๐‘ง=โˆ’2โˆ’2๐‘–โˆš3
  • D๐‘ง=โˆ’โˆš3+๐‘–, ๐‘ง=โˆš3โˆ’๐‘–, ๐‘ง=2+2๐‘–โˆš3, ๐‘ง=โˆ’2โˆ’2๐‘–โˆš3
  • E๐‘ง=โˆ’โˆš3โˆ’๐‘–, ๐‘ง=โˆš3+๐‘–, ๐‘ง=2+2๐‘–โˆš3, ๐‘ง=2โˆ’2๐‘–โˆš3

Q10:

Solve 3๐‘ง+5๐‘–๐‘งโˆ’2=0๏Šจ.

  • A๐‘ง=โˆ’23 and ๐‘ง=โˆ’1
  • B๐‘ง=โˆ’23๐‘– and ๐‘ง=๐‘–
  • C๐‘ง=23 and ๐‘ง=1
  • D๐‘ง=โˆ’23๐‘– and ๐‘ง=โˆ’๐‘–
  • E๐‘ง=23๐‘– and ๐‘ง=๐‘–

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