1. complex numbers: Review 1
1 Understand the complex number system
2 Be able to do calculations with complex numbers
3 Explore properties of complex conjugates
4 Know how to represent and use Argand diagrams
5 Solve equations with complex numbers

2. 𝑓 𝑥 =4+3𝑥 Find f(x) if: 𝑓 2−𝑖 =10−3𝑖 𝑓 𝑖−1 =1+3𝑖 𝑓 2𝑖 =4+6𝑖 𝑓 −𝑖 =4−3𝑖
Q1 of 10
𝑓 𝑥 =4+3𝑥
Find f(x) if:
𝑓 2−𝑖 =10−3𝑖
𝑓 𝑖−1 =1+3𝑖
𝑓 2𝑖 =4+6𝑖
𝑓 −𝑖 =4−3𝑖

3. −5+5𝑖 𝟏−𝟐𝒊 +(𝟏+𝒊) −𝟑+𝒊 = 𝟓−𝟓𝒊 −𝟓+𝟓𝒊 −𝟕+𝟓𝒊 −𝟕−𝟓𝒊 −𝟕−𝒊 𝒏𝒐𝒏𝒆 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆
Q2 of 10
𝟏−𝟐𝒊 +(𝟏+𝒊) −𝟑+𝒊 =
𝟓−𝟓𝒊
−𝟓+𝟓𝒊
−𝟕+𝟓𝒊
−𝟕−𝟓𝒊
= 2−𝑖 −3+𝑖 =−5+5𝑖
−𝟕−𝒊
𝒏𝒐𝒏𝒆 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆

4. 𝑓 𝑥 = 3+𝑖 𝑥 Find f(x) if: 𝑓 𝑖 =3𝑖−1 𝑓 1+𝑖 =2+4𝑖 𝑓 3−𝑖 =10 𝑓 3 =9+3𝑖
Q3 of 10
𝑓 𝑥 = 3+𝑖 𝑥
Find f(x) if:
𝑓 𝑖 =3𝑖−1
𝑓 1+𝑖 =2+4𝑖
𝑓 3−𝑖 =10
𝑓 3 =9+3𝑖

5. Which of the following is NOT true?
𝟏 𝒊 + 𝒊 𝟑 =−𝟐𝒊
Q4 of 10
Which of the following is NOT true?
𝒊 𝟒 =𝟏
𝟏 𝒊 𝟑 −𝒊=𝟎
𝟏 𝒊 + 𝒊 𝟑 =𝟎
𝟏 𝒊 𝟐 = 𝒊 𝟐
− 𝒊 𝟒 − 𝒊 𝟐 =𝟎
𝒏𝒐𝒏𝒆 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆

6. 𝑓 𝑥 =7−𝑥 Find f(x) if: 𝑓 3+2𝑖 =4−2𝑖 𝑓 1+𝑖 =6−𝑖 𝑓 3𝑖 =7−3𝑖 𝑓 −𝑖 =7+𝑖
Q5 of 10
𝑓 𝑥 =7−𝑥
Find f(x) if:
𝑓 3+2𝑖 =4−2𝑖
𝑓 1+𝑖 =6−𝑖
𝑓 3𝑖 =7−3𝑖
𝑓 −𝑖 =7+𝑖

7. 𝟏𝟑 𝟐−𝟑𝒊 𝟏𝟑 𝟐+𝟑𝒊 𝟐−𝟑𝒊 𝟏𝟑 𝟐−𝟑𝒊 𝟑+𝟐𝒊 𝒊 𝟕−𝟒𝒊 𝟐+𝒊 𝒏𝒐𝒏𝒆 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆
Q6 of 10
"Which of the following complex numbers is not equal to the others?"
𝟐−𝟑𝒊
𝟏𝟑 𝟐+𝟑𝒊
𝟏𝟑 𝟐−𝟑𝒊
𝟑+𝟐𝒊 𝒊
𝟕−𝟒𝒊 𝟐+𝒊
𝒏𝒐𝒏𝒆 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆

8. 𝑓 𝑥 =𝑖𝑥 Find f(x) if: 𝑓 1+𝑖 =−1+𝑖 𝑓 3−𝑖 =1+3𝑖 𝑓 2𝑖 =−2 𝑓 1−𝑖 =1+𝑖
Q7 of 10
𝑓 𝑥 =𝑖𝑥
Find f(x) if:
𝑓 1+𝑖 =−1+𝑖
𝑓 3−𝑖 =1+3𝑖
𝑓 2𝑖 =−2
𝑓 1−𝑖 =1+𝑖

9. Given that p+qi= 1 12−5𝑖 the values of p and q are
Q8 of 10
𝑝= , 𝑞= 5 169
Given that p+qi= 1 12−5𝑖 the values of p and q are
𝒑= 𝟓 𝟏𝟏𝟗 , 𝒒= 𝟏𝟐 𝟏𝟏𝟗
𝒑= 𝟓 𝟏𝟔𝟗 , 𝒒= 𝟏𝟐 𝟏𝟔𝟗
𝒑= 𝟏𝟐 𝟏𝟏𝟗 , 𝒒= 𝟓 𝟏𝟏𝟗
𝒑= 𝟏𝟐 𝟏𝟔𝟗 , 𝒒= 𝟓 𝟏𝟔𝟗
𝒑= 𝟏𝟐 𝟏𝟏𝟗 , 𝒒= 𝟓 𝟏𝟔𝟗
𝒏𝒐𝒏𝒆 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆

10. 𝑓 𝑥 =(2−𝑖)𝑥 Find f(x) if: 𝑓 1+𝑖 =3+𝑖 𝑓 2+3𝑖 =7+4𝑖 𝑓 1−𝑖 =1−3𝑖 𝑓 2+𝑖 =5
Q9 of 10
𝑓 𝑥 =(2−𝑖)𝑥
Find f(x) if:
𝑓 1+𝑖 =3+𝑖
𝑓 2+3𝑖 =7+4𝑖
𝑓 1−𝑖 =1−3𝑖
𝑓 2+𝑖 =5

11. Which of the following is NOT true?
Q10 of 10
𝒛 𝒛 ∗ = 𝒛 𝟐 𝒛 𝒛 ∗ not real
Which of the following is NOT true?
𝒛 𝒛 ∗ is real
𝒛+ 𝒛 ∗ is real
𝒛 𝒛 ∗ is real
𝒛− 𝒛 ∗ is pure imaginary
(𝒛 𝒛 ∗ ) ∗ is real
𝒏𝒐𝒏𝒆 𝒐𝒇 𝒕𝒉𝒆𝒔𝒆