The complex plane, and the absolute value of a complex number

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Noah has pins at 2 + 7i and -1 + 6i. Leave it as a square root. What is the distance between them?

   √10
2. 2.

   Pia's two kites sit at -4 − i and 1 + 3i. Leave it as a square root. How far apart are they?

   √41
3. 3.

   Ren's robot drives straight from 6 + 2i to 4 − 5i. Leave it as a square root. How far does it drive?

   √53
4. 4.

   Tala finds the distance between -3 + 6i and 3 + 5i. Leave it as a square root. What is the distance?

   √37
5. 5.

   Zee has two pins on a grid map, at 6 + 2i and 4 − 5i. Which is farther from 0?

   • 4 − 5i
   • 6 + 2i
   • They are the same distance from 0
6. 6.

   Esme's kites are drawn at 7 + i and 5 + 5i. Which is farther from 0?

   • They are the same distance from 0
   • 7 + i, since its real part is bigger
   • 5 + 5i
7. 7.

   Kira compares 9 − 2i and -7 + 6i on a puzzle card. Which is farther from 0?

   • They are the same distance from 0
   • -7 + 6i
   • 9 − 2i
8. 8.

   Luz starts at 1 + 2i, and the halfway point of the trip is 3 − i. Where does the trip end, in a + bi form?

   5 − 4i
9. 9.

   Noah's robot leaves 6 − 2i, and the halfway stop is 2 + i. Where does the trip end, in a + bi form?

   -2 + 4i
10. 10.

    Pia knows one end of a segment is -5 − 3i and its midpoint is i. What is the other end, in a + bi form?

    5 + 5i