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Back to Exercise: Find conjugates and quotients of complex numbers

Exercises: Find Conjugates and Quotients of Complex Numbers

Show your work. Write all answers in standard form a+bia + bi (or as simplified real numbers where appropriate).

Grade 9·19 problems·~35 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-a-3
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A

Warm-Up: Review What You Know

1

What is the result of (3+4i)(3−4i)(3 + 4i)(3 - 4i)?

2

In the division technique 12⋅22=22\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}, what principle is being applied?

3

Use the Pythagorean theorem: in a right triangle with legs 33 and 44, the hypotenuse length is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Enter a number.

B

Fluency Practice

1

What is the conjugate of −1−2i-1 - 2i?

2

Compute ∣3+4i∣|3 + 4i| (the modulus). Enter the numerical value.

3

Compute ∣1+i∣|1 + i|. Enter the exact value (simplified radical form or decimal).

4

Compute 2+3i1−2i\dfrac{2 + 3i}{1 - 2i}.

5

Compute 5+i2+3i\dfrac{5 + i}{2 + 3i}. What is the real part of the result (as a fraction)? Enter a fraction or decimal.

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