Topic-test Complex-numbers 20221 PDF

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Topic test: Complex numbers

jacaranda Topic test: Complex numbers Total marks – 29 Section A 12 marks • Attempt Questions 1 to 12 • Allow about 15 minutes for this section Section B 27 marks • Attempt Questions 13 to 15 • Allow about 30 minutes for this section

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© 2016 John Wiley & Sons Australia, Ltd

Topic test: Complex numbers

Section A – Multiple-choice questions 12 marks • •

Attempt Questions 1 to 12 Allow about 15 minutes for this section

___________________________________________________________________________

Question 1. is equal to A. B. C. D.

Mark(s) : 1

Question 2. Which of the following is not a real number? A. B.

C. D.

Mark(s) : 1

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© 2016 John Wiley & Sons Australia, Ltd

Topic test: Complex numbers Question 3.

If

then z is equal to

A. B. C. D.

Mark(s) : 1

Question 4.

If

then p is equal to

A. B. C. 6 D.

Mark(s) : 1

Question 5. For any complex number

where both x and y are real, then

is equal to

A. B. C. D.

Mark(s) : 1

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© 2016 John Wiley & Sons Australia, Ltd

Topic test: Complex numbers Question 6. The polar form of

is equal to

A.

B.

C.

D.

Mark(s) : 1

Question 7.

If

is equal to

A. B. C. 12 D.

Mark(s) : 1

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© 2016 John Wiley & Sons Australia, Ltd

Topic test: Complex numbers Question 8.

is equal to A. B. C. D.

Mark(s) : 1

Question 9. If

and

then

is equal to

A. B. C. D.

Mark(s) : 1 Question 10. The solution(s) to the equation

are

A. B. C. D.

Mark(s) : 1

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© 2016 John Wiley & Sons Australia, Ltd

Topic test: Complex numbers Question 11.

If

is equal to

A.

B.

C.

D.

Mark(s) : 1 Question 12.

For

where both x and y are real, then the complex number

is found by

A. reflecting z in the real axis B. reflecting z in the imaginary axis C. reflecting z in both the real and imaginary axis D.

rotating z through

in a clockwise direction

Mark(s) : 1

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© 2016 John Wiley & Sons Australia, Ltd

Topic test: Complex numbers

Section B – Short answer questions 27 marks •

Attempt Questions 13 to 15

•

Allow about 30 minutes for this section

___________________________________________________________________________

Question 13.

Let

and

a. Express v in Cartesian form and hence find b. Express u in polar form and hence find

c. Deduce the exact value of

Cartesian form. (4 marks)

in polar form. (4 marks)

. (3 marks)

d. Using the formula

for

, verify your exact value

. (2 marks)

Mark(s) : 13 Question 14. Find all real numbers a and b that satisfy

.

Mark(s) : 4

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© 2016 John Wiley & Sons Australia, Ltd

Topic test: Complex numbers Question 15.

a. Express the complex number find

and

c. Find

and

and hence

giving your answer in standard form. (4 marks)

b. Express the complex number find

in the form

in the form

and hence

giving your answer in standard form. (4 marks)

giving your answer in standard form. (2 marks)

Mark(s) : 10

End of Topic Test.

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