Quiz about 0B2 Week 2 Review Session - Complex Arithmetic

Question 1

What is the imaginary part of -3-4i

Accepted Answer

-4

Answer

4

Answer

-4i

Answer

-3

Question 2

Express $$\sqrt{\ -64}$$ in the form ai for some real number a.

Accepted Answer

8i

Answer

64i

Answer

-8i

Answer

-64i

Question 3

Compute (-2i)(-3i)

Accepted Answer

-6

Answer

6

Answer

6i

Answer

-6i

Question 4

Compute (-7+2i)+(3+10i).

Note: The brackets are not required here. I only put them there for clarity.

Accepted Answer

-4+12i

Answer

-10-12i

Answer

-41-64i

Answer

-4+8i

Question 5

Compute (-7+2i)(3+10i).

Note: In this case, the brackets do need to be there.

Accepted Answer

-41-64i

Answer

-10+21i

Answer

-41+20i

Answer

-21+20i

Question 6

Which of the following is the complex conjugate of 11-2i?

Accepted Answer

11+2i

Answer

-11-2i

Answer

-11+2i

Answer

11-2i

Question 7

Given u=9-3i, compute $$\overline{u}u$$ , where $$\overline{u}$$ is the complex conjugate of u.

Tip: Make a note of your answer because you will need it for the next question.

Accepted Answer

90

Answer

72-54i

Answer

72+54i

Answer

72

Question 8

Hence (i.e. using the answer to the previous question) compute $$\left(9-3i\right)^{-1}$$ .

Tip: Make a note of your answer because you will need it for the next question.

Accepted Answer

$$\frac{1}{10}+\frac{1}{30}i$$

Answer

$$\frac{1}{9}-\frac{1}{3}i$$

Answer

$$\frac{1}{10}-\frac{1}{30}i$$

Answer

$$10+30i$$

Question 9

Hence, compute $$\frac{5-3i}{9-3i}$$ .

Accepted Answer

$$\frac{18}{30}-\frac{4}{30}i$$

Accepted Answer

$$\frac{3}{5}-\frac{2}{15}i$$

Answer

$$\frac{12}{30}-\frac{14}{30}i$$

Answer

$$\frac{2}{5}+\frac{7}{15}i$$

0B2 Week 2 Review Session - Complex Arithmetic

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