Imaginary Numbers Review Lesson Slides: 6 Slides (Grade 12)

6 Slides • 6 Questions

1

The Imaginary Numbers

2

What are imaginary numbers?

Equations such as
$x^2+1=0$ have no real solutions, so mathematicians defined imaginary numbers to represent their solutions.
$i=\sqrt{-1}$ This is useful when working with square roots of negative numbers
An imaginary number is written in the form $bi$ , where $i$ is the imaginary part and b is the real part

3

Let's work one together!

\sqrt{-5}

Rewrite $\sqrt{-x}$ as $\sqrt{-1\times x}$
Break x down if it is not a perfect square
Simplify the radical, recall that $i=\sqrt{-1}$

4

Multiple Choice

Your Turn!

\sqrt{-9}

1

$\pm3$

2

$\pm3i$

3

$\pm9i$

4

$\pm9$

5

Multiple Choice

$x^2+81=0$

1

$\pm\sqrt{9i}$

2

$\pm9$

3

$\pm9i$

4

$\pm3i$

6

Now let's look at the powers of

i

$i=\sqrt{-1}$
$i^2=-1$
$i^3=-i$
$i^4=1$

7

$i^{15}$

How do you think you would solve this?

8

Multiple Choice

Your Turn!

i^{22}

1

$\sqrt{-1}$

2

$-1$

3

$-i$

4

1

9

Product of Imaginary Numbers

\sqrt{-18}\cdot\sqrt{-10}

First take the $i$ out of the radical then solve

10

Multiple Choice

$\sqrt{-8}\cdot\sqrt{24}$

1

$i\sqrt{24}$

2

$8\sqrt{3}$

3

$8i\sqrt{3}$

4

$60i$

11

Multiple Choice

$4i\cdot7i$

1

$28i$

2

-28

3

28

4

$14i$

12

Multiple Choice

$\left(2i\right)^3\cdot\left(5i\right)$

1

40

2

$40i$

3

10

4

$10i$

The Imaginary Numbers

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