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Cogito

Algebra 2 · Chapter 2 · Lesson 1

Practice Worksheet

Complex Numbers

What happens when the discriminant is negative.

10 problems · about 20 minutes · N-CN.A.1, N-CN.A.2, N-CN.C.7

NameDate

Figure — use these to answer the problems

Lift the parabola clear of the axis. It has no real roots, but it still has two.
-8-8-6-6-4-4-2-222446688
y = 1x² + 0x + 2
a1
b0
c2
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Composition and Inverse Functions”

    f(x) = x − 7. What is f⁻¹(3)?

    Answer

  2. From “Piecewise and Absolute Value Functions”

    y = |x − 7| + 3. What is the minimum value?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. x² = −25. What is the coefficient of i in the positive root?

    Answer

  2. What is i defined to be?

    • The number whose square is −1.
    • A very large number.

  3. (2 + 3i) + (4 + 5i). Imaginary part?

    Answer

  4. What is i⁴?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. (6 + 7i) − (2 + 3i). Real part?

    Answer

  2. x² = −9. What is the coefficient of i in the positive root?

    Answer

Stretch Yourself

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

2 problems

  1. The Square

    What is i²?

    Answer

  2. Adding

    (3 + 2i) + (5 + 4i). What is the real part?

    Answer