MATH1015 Revision Session

If we have two complex numbers such that a = 2 + i and b = -3 - 2i, find a + b

• -1 - i
• -1 - 2i
• -5 - i
• -1 + i

a = 2cis(30)

b = 3cis(20)

Find a x b

• 7cis(60)
• 4cis(10)
• 6cis(50)
• 5cis(40)

Convert the following to polar form:

2 + i

• √5cis(26.57)

• 5cis(26.57)

• √5cis(153.43)

• 5cis(153.43)

What is the centre and radius of the following complex region:

|z + 4| > 3

• Center: (0,0) Radius: 4

• Center: (-3,0) Radius: 2

• Center: (-4,0) Radius: 3

• Center: (-5,0) Radius: 5

Draw the following complex region:

Im(z) < 2

• y > 2 

  Area above line y = 2

• x < 2 

  Area below line x = 2

• y < 2 

  Area below line y = 2

• x > 2 

  Area above line y = 2

Find the dot/scalar product between:

[1, 2, 1] and [3, 6, 8]

• 15
• 23
• 18
• 30

Find the unit vector of:

[2, 1, 3]

• [0.5, 0.5, 0.5]
• [0, 1, 0]

Find the cross product between:

[0, 1, 1] and [2, 1, 0]

• [-1, 2, -2]
• [1, 0, 2]
• [1, 2, -2]

• [1, 2, 2]

Find the angle between:

[3, 1, 2] and [-2, 2, 2]

• 180 degrees
• 45 degrees
• 90 degrees
• 60 degrees

What does the cross product of two vectors actually represent?

• A vector that lies in the same plane as the two vectors.
• A scalar value representing the length of the vectors.
• A vector perpendicular to the plane of the two vectors, with magnitude equal to the area of the parallelogram they form.
• The sum of the two vectors represented as a single vector.