Exercises for Question Type 2: Multiplying by a conjugate

Question 1

Skill question

Find the real number $x$ such that $\frac{x + 2 i}{4 + 3 i}$ is purely real.

[4]

Question 2

Skill question

Let $z = 4 + 3 i$ . Find the complex number $w$ with $∣ w ∣ = 1$ such that $w z$ is real and positive.

[3]

Question 3

Skill question

Express $\frac{7 + 5 i}{4 + 3 i}$ in the form $a + bi$ .

[4]

Question 4

Skill question

Evaluate $\frac{2}{4 + 3 i} + \frac{3}{4 - 3 i}$ in the form $a + bi$ .

[3]

Question 5

Skill question

Find the value of $\frac{1}{4 + 3 i} - \frac{1}{4 - 3 i}$ .

[3]

Question 6

Skill question

Simplify $\frac{1}{( 4 + 3 i ) ^{2}}$ to the form $a + bi$ .

[4]

Question 7

Skill question

Find the conjugate of $4 + 3 i$ and compute $(4 + 3 i) (4 - 3 i)$ .

[3]

Question 8

Skill question

Compute $\frac{1}{4 + 3 i} + \frac{1}{4 - 3 i}$ .

[2]

Question 9

Skill question

Simplify $\frac{4 + 3 i}{4 - 3 i}$ to the form $a + bi$ .

[4]

Question 10

Skill question

Simplify $\frac{7 - 2 i}{4 + 3 i} + \frac{7 + 2 i}{4 - 3 i}$ to the form $a + bi$ .

[4]

Question 11

Skill question

Express $\frac{1}{4 + 3 i}$ in the form $a + bi$ .

[4]

IB Mathematics Analysis and Approaches Question Type 2: Multiplying by a Conjugate Exercises