Where do we learn about the fact that (i^2) = -1?

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Course: Test Everything QE Sandbox > Unit 1

Lesson 6: Expression

Expression article

Excerpt from "Complex number operations review" article. Includes EXPRESSION widget only.

Practice set 2: Multiplying complex numbers

When multiplying complex numbers, we perform a multiplication similar to how we expand the parentheses in binomial products:

(a + b) (c + d) = a c + a d + b c + b d

Unlike regular binomial multiplication, with complex numbers we also consider the fact that

i^{2} = - 1

Example 1

\begin{aligned} 2 \cdot (- 3 + 4 i) \\ = 2 \cdot (- 3) + 2 \cdot 4 i \\ = - 6 + 8 i \end{aligned}

Example 2

\begin{aligned} 3 i \cdot (1 - 5 i) \\ = 3 i \cdot 1 + 3 i \cdot (- 5) i \\ = 3 i - 15 i^{2} \\ = 3 i - 15 (- 1) \\ = 15 + 3 i \end{aligned}

Example 3

\begin{aligned} (2 + 3 i) \cdot (1 - 5 i) \\ = 2 \cdot 1 + 2 \cdot (- 5) i + 3 i \cdot 1 + 3 i \cdot (- 5) i \\ = 2 - 10 i + 3 i - 15 i^{2} \\ = 2 - 7 i - 15 (- 1) \\ = 17 - 7 i \end{aligned}

Practice Problem

8 \cdot (11 i + 2) =

Your answer should be a complex number in the form $a + b i$ ‍ where $a$ ‍ and $b$ ‍ are real numbers.

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Meriwether Lewis
Posted 5 years ago. Direct link to Meriwether Lewis's post “Where do we learn about t...”
Where do we learn about the fact that (i^2) = -1?
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- Achievement Hunter
  Posted 4 years ago. Direct link to Achievement Hunter's post “This is the best answer, ...”
  This is the best answer, everyone thinks so!
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William Clark
Posted 2 years ago. Direct link to William Clark's post “*Testing* _the_ 'formatti...”
Testing the 'formatting' options.
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Masamune Date
Posted 2 years ago. Direct link to Masamune Date's post “Adding questions to test ...”
Adding questions to test the pagination of comments/questions.
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Erdrick Loto
Posted 2 years ago. Direct link to Erdrick Loto's post “Why does the expression w...”
Why does the expression widget only show addition, subtraction, multiplication, and division?
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Erdrick Loto
Posted 3 years ago. Direct link to Erdrick Loto's post “Testing the new avatars i...”
Testing the new avatars in discussion areas.
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Cloud Strife
Posted 2 years ago. Direct link to Cloud Strife's post “For the question we have ...”
For the question we have to multiply it out, but then leave the addition, meaning we don't end with the answer, but another problem.
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John Silver
Posted 2 years ago. Direct link to John Silver's post “*How many words can you p...”
How many words can you put inside the formatting characters
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Tifa Lockhart
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What if I choose to have the green leaf as my avatar?
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Web Mobil
Posted 2 years ago. Direct link to Web Mobil's post “`What does the code forma...”
What does the code format look like
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Zetian Wu
Posted 2 years ago. Direct link to Zetian Wu's post “_Italics in a sentence bu...”
Italics in a sentence but only if you do not have other punctuation in the text
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