Points, distances, and turns

Mathematics · Algebra · ages 17-18

Name ______________________ Date ____________

What is the modulus of 3 + 4i?
Answer: ______________
Kim multiplies 1 + i by i and gets -1 + i, calling it a quarter turn anticlockwise. Is Kim right?
Circle one: True False
What is the modulus of 3 + 4i?
Answer: ______________
Which point represents 3 + 4i on the Argand plane?
- (4, 3)
- (3, 4)
- (-3, 4)
Leo says 4 - 3i lies in the fourth quadrant, with positive real part and negative imaginary part. Is Leo right?
Circle one: True False
Which number has modulus 2 and argument 90 degrees?
- 2
- 2i
- -2
- -2i
What is the argument of 1 + i in degrees, taking values between -180 and 180?
Answer: ______________
Which number has modulus 2 and argument 90 degrees?
- 2
- -2
- 2i
What is (1 + i) squared?
- 2
- 2i
- -2
Multiplying any z by i twice sends z to -z, which is a half turn about the origin. True or false?
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

5 · Root of 9 + 16 is root of 25, which is 5.
True · Kim is right. (1 + i)i = i + i squared = -1 + i, a 90 degree rotation of the point (1, 1).
5 · The modulus is 5, since sqrt(9 + 16) = 5.
(3, 4) · Real 3 goes across and imaginary 4 goes up: (3, 4).
True · Leo is right. Positive real with negative imaginary is exactly the fourth quadrant.
2i · 2i. It sits two units up the imaginary axis, at a right angle to the positive real axis.
45 · 45 degrees. The point (1, 1) sits on the diagonal, making equal angles with both axes.
2i · Two units up the imaginary axis sits at a right angle to the real axis.
2i · Expanding gives 1 + 2i + i squared, and i squared cancels the 1.
True · True. Two quarter turns make a half turn, and i squared = -1 negates the number.