Worksheet: Dividing Complex Numbers

In this worksheet, we will practice performing division on complex numbers.

Q1:

Simplify 23+𝑖.

  • A(3𝑖)10
  • B(3𝑖)5
  • C3𝑖
  • D23+2𝑖
  • E232𝑖

Q2:

Put 189𝑖3𝑖 in the form 𝑎+𝑏𝑖.

  • A3+6𝑖
  • B2754𝑖
  • C3+54𝑖
  • D9+18𝑖

Q3:

Simplify 36𝑖15𝑖.

  • A3326+926𝑖
  • B913526𝑖
  • C11838𝑖
  • D34+524𝑖
  • E3+65𝑖

Q4:

Simplify 4+𝑖4𝑖.

  • A1𝑖
  • B15+8𝑖17
  • C15+8𝑖15
  • D1715+8𝑖
  • E17+8𝑖15

Q5:

Express (5+5𝑖)(84𝑖)1𝑖 in the form 𝑎+𝑏𝑖.

  • A4020𝑖
  • B5+40𝑖
  • C28+16𝑖
  • D20+40𝑖
  • E60+20𝑖

Q6:

Simplify 124𝑖2𝑖.

  • A2+24𝑖
  • B4+12𝑖
  • C2+6𝑖
  • D824𝑖

Q7:

Put 25+5𝑖 in the form 𝑎+𝑏𝑖.

  • A0.20.2𝑖
  • B0.20.2𝑖
  • C0.2+0.2𝑖
  • D0.2+0.2𝑖

Q8:

Simplify 1313+2𝑖.

  • A169165+26165𝑖
  • B169173+26173𝑖
  • C16916526165𝑖
  • D16917326173𝑖

Q9:

Simplify (8+7𝑖)(1+8𝑖)(6+4𝑖).

  • A11330926𝑖
  • B15+30910𝑖
  • C1530910𝑖
  • D113+30926𝑖

Q10:

Simplify (3+2𝑖)(3+3𝑖)(4+𝑖)(4+4𝑖).

  • A15343368𝑖
  • B15343368𝑖
  • C1534+3368𝑖
  • D1534+3368𝑖

Q11:

Simplify 19𝑖+5𝑖7𝑖6+4𝑖4𝑖+2𝑖.

  • A12𝑖
  • B1+2𝑖
  • C1+𝑖
  • D1𝑖

Q12:

Simplify 7+𝑖+3𝑖6𝑖2𝑖𝑖𝑖.

  • A4+3𝑖
  • B43𝑖
  • C107𝑖
  • D10+7𝑖

Q13:

Solve the equation 𝑖𝑧=4+3𝑖.

  • A𝑧=4+3𝑖
  • B𝑧=34𝑖
  • C𝑧=3+4𝑖
  • D𝑧=3+4𝑖
  • E𝑧=34𝑖

Q14:

If 𝑎+𝑏𝑖=35𝑖3+5𝑖, is it true that 𝑎+𝑏=1?

  • Ayes
  • Bno

Q15:

Find the real values of 𝑥 and 𝑦 that satisfy the equation 79𝑖12𝑖=𝑥+𝑦𝑖.

  • A𝑥=5, 𝑦=1
  • B𝑥=253, 𝑦=53
  • C𝑥=7, 𝑦=92
  • D𝑥=635, 𝑦=25
  • E𝑥=21, 𝑦=23

Q16:

Put 43+3238 in the form 𝑎+𝑏𝑖.

  • A4111211𝑖
  • B411+126𝑖
  • C41112611𝑖
  • D411+12611𝑖
  • E411+1211𝑖

Q17:

By what complex number would you multiply the numerator and denominator of the quotient 5+6𝑖32𝑖 in order to simplify it?

  • A32𝑖
  • B3+2𝑖
  • C5+6𝑖
  • D32𝑖
  • E56𝑖

Q18:

Simplify 7(4+𝑖).

  • A105289+56289𝑖
  • B10528956289𝑖
  • C105241+28241𝑖
  • D10528956289𝑖

Q19:

Expand and simplify (𝑝+𝑞𝑖)(𝑝𝑞𝑖).

  • A𝑞𝑝
  • B𝑝+𝑞
  • C(𝑝+𝑞)
  • D𝑝𝑞
  • E(𝑝𝑞)

Expand (𝑎+𝑏𝑖)(𝑝𝑞𝑖).

  • A(𝑎𝑝𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖
  • B(𝑎𝑝𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖
  • C(𝑎𝑞+𝑏𝑝)+(𝑏𝑞𝑎𝑝)𝑖
  • D(𝑎𝑝+𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖
  • E(𝑎𝑝+𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖

Hence, find a fraction which is equivalent to 𝑎+𝑏𝑖𝑝+𝑞𝑖 and whose denominator is real.

  • A(𝑎𝑝+𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖𝑝𝑞
  • B(𝑎𝑝+𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖𝑝+𝑞
  • C(𝑎𝑝+𝑏𝑞)(𝑏𝑝𝑎𝑞)𝑖𝑝𝑞
  • D(𝑎𝑝+𝑏𝑞)+(𝑏𝑝𝑎𝑞)𝑖𝑝+𝑞
  • E(𝑎𝑞+𝑏𝑝)+(𝑏𝑞𝑎𝑝)𝑖𝑝+𝑞

Q20:

Simplify 2+4𝑖𝑖.

  • A4+2𝑖
  • B2+4𝑖
  • C42𝑖
  • D42𝑖
  • E24𝑖

Q21:

Solve the equation 𝑧(2+𝑖)=3𝑖 for 𝑧.

  • A𝑧=1+𝑖2
  • B𝑧=1𝑖2
  • C𝑧=1𝑖
  • D𝑧=1+𝑖
  • E𝑧=32𝑖

Q22:

Put 1+2𝑖9+7𝑖 in the form 𝑥+𝑦𝑖.

  • A2332+1132𝑖
  • B23130+11130𝑖
  • C2313011130𝑖
  • D23321132𝑖

Q23:

Put 12𝑖(1+𝑖) in the form 𝑥+𝑦𝑖.

Q24:

Simplify 22𝑖3𝑖.

  • A232𝑖
  • B12+4𝑖5
  • C22𝑖5
  • D42𝑖5
  • E24𝑖5

Q25:

Express 1(3+𝑖) in the form 𝑎+𝑏𝑖.

  • A45+35𝑖
  • B225350𝑖
  • C225+350𝑖
  • D225+350𝑖
  • E4535𝑖

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