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

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

−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

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

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

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

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

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

Given that p+qi= 1 12−5𝑖 the values of p and q are Q8 of 10 𝑝= 12 169 , 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

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

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