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Cogito

Integrated Math 2 · Chapter 3 · Lesson 1

Practice Worksheet

The Imaginary Unit

A square root that had to be invented.

12 problems · about 20 minutes · N-CN.A.1

NameDate

Figure — use these to answer the problems

A complex number is a point on this plane: real part across, imaginary part up.
  • Vector a(3, 4) · length 5
Real part3
Imaginary part4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. √(−36) = ki. What is k?

    Answer

  2. Why was i introduced?

    • No real number squares to a negative, so some equations had no solutions.
    • To make algebra shorter to write.

  3. √(−25) = ki. What is k?

    Answer

  4. √(−49) = ki. What is k?

    Answer

  5. What is i⁴?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. What is i⁸?

    Answer

  2. For i²³, what is the remainder when 23 is divided by 4?

    Answer

  3. For 3 + 5i, what is the real part?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Match each power of i with its value.

    Draw a line from each item on the left to its match on the right.

    • i squared
    • i to the fourth
    • i cubed
    • Negative one
    • One
    • Negative i

  2. √(−81) = ki. What is k?

    Answer

  3. The Root

    √(−16) = ki. What is k?

    Answer

  4. The Square

    What is i² ?

    Answer