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Common Core (The Complex Number System)

Common Core for Mathematics

### Suggested Learning Targets

### Imaginary and Complex Numbers

Imaginary Numbers Introduction

i^{2} = − 1

Solving Equations with i in the solution.
**What Are Complex Numbers?**

Imaginary Number: Square is a nonpositive real number

Complex Number: Square is a nonnegative real number

0 is both a complex and an imaginary number

Complex number has the form*a + bi* with *a* and *b* real

How to plot complex numbers on the Cartesian plane?

**Introduction to i and Imaginary Numbers**
### Square Root of Negative Numbers

Simplifying Square Roots of Negative Numbers Using i.
**Expressing Square Roots of Negative Numbers with i**

This video looks at simplifying square roots with negative numbers using the imaginary unit i. It includes 6 examples.### Rewrite Powers of i

Calculating i Raised to Arbitrary Exponents.
**Rewriting Powers of ' i ' - Ex 1**

Complex number ' i ', raise it to some different powers, and simplify.**Rewriting Powers of ' i ' - Ex 2**

i raise to a negative power.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core (The Complex Number System)

Common Core for Mathematics

Videos and lessons to help High School students know there is a complex number *i* such that *i*^{2} = –1, and every complex number has the form *a + bi* with *a* and *b* real.

- I know what are imaginary numbers and complex numbers.
- I can write complex number in the form
*a + bi*with*a*and*b*real. - I can simplify square roots of negative numbers using i.
- I can rewrite arbitrary powers of i.

i

Solving Equations with i in the solution.

Imaginary Number: Square is a nonpositive real number

Complex Number: Square is a nonnegative real number

0 is both a complex and an imaginary number

Complex number has the form

How to plot complex numbers on the Cartesian plane?

This video looks at simplifying square roots with negative numbers using the imaginary unit i. It includes 6 examples.

Complex number ' i ', raise it to some different powers, and simplify.

i raise to a negative power.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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