Question Type 2: Multiplying by a conjugate Exercises

Question 1

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

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Question 2

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

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Question 3

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

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Question 4

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

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Question 5

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

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Question 6

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

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Question 7

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

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Question 8

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

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Question 9

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

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Question 10

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

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Question 11

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

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