More Arithmetic with Complex Numbers: IM Alg2.3.14
[url=https://im.kendallhunt.com/HS/teachers/3/3/14/preparation.html]“More Arithmetic with Complex Numbers”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.3.14 Lesson
- IM Alg2.3.14 Lesson: More Arithmetic with Complex Numbers
- Alg2.3.14 Practice
- IM Alg2.3.14 Practice: More Arithmetic with Complex Numbers
IM Alg2.3.14 Lesson: More Arithmetic with Complex Numbers
Which one doesn’t belong?
A. [math]i^2[/math][br]B. [math](1+i)+(1-i)[/math][br]C. [math](1+i)^2[/math][br]D. [math](1+i)(1-i)[/math]
Write each power of i in the form a+bi, where a and b are real numbers. If a or b is zero, you can ignore that part of the number. For example, 0+3i can simply be expressed as 3i.
What is [math]i^{100}[/math]? Explain your reasoning.[br]
What is [math]i^{38}[/math]? Explain your reasoning.[br]
Write each power of 1+i in the form a+bi, where a and b are real numbers. If a or b is zero, you can ignore that part of the number. For example, 0+3i can simply be expressed as 3i.
Compare and contrast the powers of [math]1+i[/math] with the powers of [math]i[/math]. What is the same? What is different?[br]
For each row, your partner and you will each rewrite an expression so it has the form a+bi, where a and b are real numbers. You and your partner should get the same answer. If you disagree, work to reach agreement.
IM Alg2.3.14 Practice: More Arithmetic with Complex Numbers
[size=150]Select [b]all[/b] expressions that are equivalent to [math]8+16i[/math].[/size]
[size=150]Which expression is equivalent to [math](\text{-}4+3i)(2-7i)[/math]?[/size]
Match the equivalent expressions.
Write each expression in a+bi form.
[math](\text{-}8+3i)-(2+5i)[/math]
[math]7i(4-i)[/math]
[math](3i)^3[/math]
[math](3+5i)(4+3i)[/math]
[math](3i)(\text{-}2i)(4i)[/math]
[size=150]Here is a method for solving the equation [math]\sqrt{5+x}+10=6[/math]. Does the method produce the correct solution to the equation? Explain how you know.[br][math]\begin{align} \sqrt{5+x}+10 &= 6 \\ \sqrt{5+x} &= \text-4 &\text{ (after subtracting 10 from each side)} \\ 5+x &= 16 &\text{ (after squaring both sides)} \\ x &= 11 \\ \end{align}[/math][br][/size]
Write each expression in the form , where a and b are real numbers.a+bi
[math]4(3-i)[/math]
[math](4+2i)+(8-2i)[/math]
[math](1+3i)(4+i)[/math]
[math]i(3+5i)[/math]
[math]2i\cdot7i[/math]