Worksheet: Multiplying Complex Numbers

In this worksheet, we will practice multiplying two complex numbers.

Q1:

Expand and simplify (4𝑖)(3+2𝑖).

  • A14+5𝑖
  • B12+3𝑖
  • C122𝑖
  • D12+7𝑖
  • E10+5𝑖

Q2:

Multiply (3+𝑖) by (2+5𝑖).

  • A6+5𝑖
  • B618𝑖
  • C113𝑖
  • D68𝑖
  • E1113𝑖

Q3:

What is 7𝑖(5+5𝑖)?

  • A3535𝑖
  • B3535𝑖
  • C35+35𝑖
  • D35+35𝑖

Q4:

What is (9+5𝑖)(3𝑖)?

  • A22+24𝑖
  • B32+24𝑖
  • C2224𝑖
  • D5𝑖+24𝑖27
  • E275𝑖

Q5:

Simplify (7+6𝑖)(29𝑖).

  • A4051𝑖
  • B40+75𝑖
  • C68+51𝑖
  • D6851𝑖
  • E68+75𝑖

Q6:

If 𝑟=2+7𝑖 and 𝑠=1+2𝑖, what is 𝑟×𝑠?

  • A2+25𝑖
  • B2+14𝑖
  • C12+11𝑖
  • D16+11𝑖
  • E23𝑖

Q7:

Simplify (36𝑖)(2𝑖).

  • A15𝑖
  • B2537𝑖
  • C811𝑖
  • D9045𝑖
  • E2736𝑖

Q8:

If 𝑟=2+𝑖, express 𝑟 in the form 𝑎+𝑏𝑖.

  • A6+7𝑖
  • B2+11𝑖
  • C8+𝑖
  • D112𝑖
  • E8𝑖

Q9:

Given that 𝑍=535𝑖, determine the algebraic form of 𝑍.

  • A50+503𝑖
  • B50503𝑖
  • C50503𝑖
  • D50+503𝑖

Q10:

Simplify 5𝑖5𝑖5𝑖.

  • A13026𝑖
  • B10616𝑖
  • C13026𝑖
  • D130+26𝑖

Q11:

Simplify 17111117.

  • A28𝑖
  • B168374𝑖
  • C28𝑖
  • D168+374𝑖

Q12:

Calculate 8+28828.

Q13:

Simplify (118𝑖)(11+8𝑖)+(136𝑖)(13+6𝑖).

Q14:

What is (5𝑖)?

  • A2410𝑖
  • B102𝑖
  • C26
  • D24+10𝑖

Q15:

What is 92𝑖77𝑖+9𝑖?

  • A14+49𝑖
  • B270𝑖
  • C147𝑖
  • D57𝑖
  • E42+49𝑖

Q16:

Simplify 65𝑖.

  • A1160𝑖
  • B11+60𝑖
  • C234+415𝑖
  • D234415𝑖
  • E415+234𝑖

Q17:

Compute the product of 2+3𝑖 and 4+6𝑖.

  • A6+9𝑖
  • B10+24𝑖
  • C2+3𝑖
  • D2

Q18:

If 𝑟=2+4𝑖 and 𝑠=8𝑖, find (𝑟𝑠).

  • A75100𝑖
  • B100+25𝑖
  • C125100𝑖
  • D75
  • E10075𝑖

Q19:

What is (27𝑖)+(43𝑖)?

  • A4125𝑖
  • B4528𝑖
  • C4131𝑖
  • D4931𝑖
  • E210𝑖

Q20:

Determine all the real values of 𝑥 and 𝑦 that satisfy the equation 86𝑖=(𝑥22𝑖)(𝑦𝑖)38.

  • A𝑥=1011,𝑦=665 or 𝑥=3,𝑦=4
  • B𝑥=66,𝑦=665 or 𝑥=20,𝑦=4
  • C𝑥=66,𝑦=1011 or 𝑥=20,𝑦=3
  • D𝑥=1011,𝑦=665 or 𝑥=3,𝑦=4

Q21:

If 𝑟=45𝑖, find 𝑟.

  • A1665𝑖
  • B940𝑖
  • C4140𝑖
  • D16+25𝑖
  • E1615𝑖

Q22:

If 𝑧=12𝑖 and 𝑧=12+2𝑖, is it true that 𝑧=𝑧?

  • Ano
  • Byes

Q23:

Given that (𝑥+𝑦𝑖)(2𝑖)+(5𝑥2𝑦𝑖)(2+𝑖)=18, where 𝑥 and 𝑦 are real numbers, find the value of 𝑥 and the value of 𝑦.

  • A𝑥=1, 𝑦=2
  • B𝑥=1, 𝑦=2
  • C𝑥=1, 𝑦=4
  • D𝑥=1, 𝑦=0

Q24:

Given that 𝑥+𝑦𝑖=(2𝑖), where 𝑥 and 𝑦 are real numbers, find the value of 𝑥 and the value of 𝑦.

  • A𝑥=2, 𝑦=1
  • B𝑥=3, 𝑦=4
  • C𝑥=2, 𝑦=11
  • D𝑥=2, 𝑦=11
  • E𝑥=3, 𝑦=4

Q25:

Given that 3𝑥4𝑦𝑖=(4+𝑖), where 𝑥 and 𝑦 are real numbers, find the value of 𝑥 and the value of 𝑦.

  • A𝑥=16, 𝑦=1
  • B𝑥=5, 𝑦=2
  • C𝑥=5, 𝑦=2
  • D𝑥=4, 𝑦=1
  • E𝑥=4, 𝑦=1

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.