به انگلیسی

Points, distances, and turns

Mathematics · Algebra · ages 17-18

Name ______________________ Date ____________

What is the modulus of 6 + 8i?
Answer: ______________
Kim says the point (0, -4) on the Argand plane stands for the complex number -4i. Is Kim right?
Circle one: True False
What is the modulus of -9 + 12i?
Answer: ______________
Which point represents -2 + 5i on the Argand plane?
- (5, -2)
- (-2, 5)
- (2, 5)
Leo says -4 + 4i has argument -45 degrees, because tan θ = -1. Is Leo right?
Circle one: True False
Which is 4(cos 90° + i sin 90°) in a + bi form?
- 4
- 4i
- -4
- -4i
What is the argument of 1 - i in degrees, between -180 and 180?
Answer: ______________
Which number has modulus 3 and argument 180 degrees?
- 3
- 3i
- -3
What is (1 - i) squared?
- 2i
- -2i
- -2
Multiplying a complex number by i does not change its modulus.
Circle one: True False

Answer key

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

10 · Root of 36 + 64 is root of 100, which is 10.
True · Real part 0 and imaginary part -4 give 0 - 4i, which is -4i.
15 · 81 + 144 = 225, and root of 225 is 15.
(-2, 5) · Real -2 goes across to the left and imaginary 5 goes up: (-2, 5).
False · tan θ = -1 fits both -45 and 135 degrees. The point (-4, 4) is up and to the left, so its argument is 135 degrees, not -45.
4i · cos 90° = 0 and sin 90° = 1, so the number is 4(0 + i) = 4i.
-45 · The point (1, -1) is right and down, in the fourth quadrant, at 45 degrees below the real axis: -45 degrees.
-3 · Three units along the negative real axis is -3.
-2i · Expanding gives 1 - 2i + i squared, and i squared cancels the 1.
True · Multiplying by i is a quarter turn about the origin, and a turn keeps every distance from the origin the same.