به انگلیسی

Numbers beyond the number line

Mathematics · Algebra · ages 17-18

Name ______________________ Date ____________

What are the roots of x squared + 4 = 0, in a + bi form?
- 2i and -2i
- 2 and -2
- 4i and -4i
Sam says (4 - 2i) minus (1 + 3i) equals 3 - 5i. Is Sam right?
Circle one: True False
What are the roots of x squared + 25 = 0? Write them in a + bi form.
- 5 and -5
- 25i and -25i
- 5i and -5i
- i and -i
What is (3 + 2i) + (1 + 4i)?
- 4 - 6i
- 5 + 5i
- 4 + 6i
What is the distance from the origin to the point 3 + 4i in the complex plane?
Answer: ______________
What is (2 + i) divided by (1 + i)?
- 2
- 1.5 - 0.5i
- 1.5 + 0.5i
- 2 + i
What is (2 + 5i)(2 - 5i)?
- 29
- -21
- 4 - 25i
- 21
What is i to the power 4? Give your answer as a number.
Answer: ______________
Tom expands (1 + i) squared as 1 + i squared = 0 and stops. What is his mistake?
- He used the wrong conjugate
- He dropped the middle term 2i
- He added instead of multiplying
The equation x squared + 9 = 0 has roots 3i and -3i. What is the product of the two roots?
Answer: ______________

Answer key

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

2i and -2i · x squared = -4, so x is plus or minus the square root of -4: 2i or -2i.
True · Sam is right: 4 - 1 = 3 and -2i - 3i = -5i, so the answer is 3 - 5i.
5i and -5i · x squared = -25, so x = plus or minus the square root of -25, which is plus or minus 5i.
4 + 6i · Add reals 3 + 1 = 4 and imaginaries 2 + 4 = 6, giving 4 + 6i.
5 · The distance is the square root of (9 + 16) = the square root of 25 = 5.
1.5 - 0.5i · Multiply top and bottom by (1 - i): the top becomes 3 - i and the bottom becomes 2, so the answer is 1.5 - 0.5i.
29 · Multiply out: 4 - 10i + 10i - 25i squared = 4 + 25 = 29, since i squared is -1.
1 · i to the 4th is i squared times i squared: (-1) times (-1) = 1.
He dropped the middle term 2i · Full expansion gives 1 + 2i + i squared, which simplifies to 2i, not 0.
9 · 3i times -3i is -9 times i squared, and -9 times -1 is 9.