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Worksheet: Graphing Complex Numbers

Q1:

In which quadrant of the Argand diagram does the complex number lie?

  • A second
  • B third
  • C first
  • D fourth

Q2:

If the number is represented on Argand diagram by the point , determine the Cartesian coordinates of that point.

  • A
  • B
  • C
  • D

Q3:

If the number is represented on Argand diagram by the point , determine the Cartesian coordinates of that point.

  • A
  • B
  • C
  • D

Q4:

If the number is represented on Argand diagram by the point , determine the Cartesian coordinates of that point.

  • A
  • B
  • C
  • D

Q5:

If the number is represented on Argand diagram by the point , determine the Cartesian coordinates of that point.

  • A
  • B
  • C
  • D

Q6:

What does the modulus of a complex number represent?

  • A the angle it makes with the positive imaginary axis
  • B the angle it makes with the positive real axis
  • C its real coordinate in the complex plane
  • D its distance from the origin in the complex plane
  • E its imaginary coordinate in the complex plane

Q7:

Given that the complex number is represented by the point on the Argand diagram below, find .

  • A
  • B
  • C
  • D
  • E

Q8:

Given that the complex number is represented by the point on the Argand diagram below, find .

  • A
  • B
  • C
  • D
  • E

Q9:

Given that the complex number is represented by the point on the Argand diagram below, find .

  • A
  • B
  • C
  • D
  • E

Q10:

Given that the complex number is represented by the point on the Argand diagram below, find .

  • A
  • B
  • C
  • D
  • E

Q11:

Given that , find .

  • A
  • B
  • C
  • D
  • E

Q12:

Given that , find .

  • A
  • B
  • C
  • D
  • E

Q13:

Given that , find .

  • A
  • B
  • C
  • D
  • E

Q14:

Given that , determine the real part of the complex number .

  • A6
  • B3
  • C
  • D

Q15:

What complex number lies at the midpoint of and on the given complex plane?

  • A
  • B
  • C
  • D
  • E

Q16:

The Argand diagram shows the complex numbers , , , and . Which of these numbers is ?

  • A
  • B
  • C
  • D

Q17:

Let us consider a complex number, , with nonzero real and imaginary parts.

If the real and imaginary parts of are of the same sign, in which quadrant(s) of the Argand diagram could appear?

  • A1st or 2nd
  • B2nd or 4th
  • C3rd or 4th
  • D1st or 3rd
  • E1st or 4th

If the real and imaginary parts of are of opposite signs, in which quadrant(s) of the Argand diagram could appear?

  • A2nd or 4th
  • B3rd or 4th
  • C1st or 2nd
  • D1st or 3rd
  • E1st or 4th