Lin says, "When you add or multiply two complex numbers, you will always get an answer you can write in a+bi form." Noah says, "I don't think so. Here are some exceptions I found:" (7+2i) + (3-2i) = 10 (2+2i)(2+2i) = 8i 1. Check Noah's arithmetic. Is it correct? 2. Can Noah's answers be written in the form a, where b and are real numbers? Explain or show your reasoning.

Lin says, "When you add or multiply two complex numbers, you will always get an answer you can write in a+bi form." Noah says, "I don't think so. Here are some exceptions I found:" (7+2i) + (3-2i) = 10 (2+2i)(2+2i) = 8i 1. Check Noah's arithmetic. Is it correct? 2. Can Noah's answers be written in the form a, where b and are real numbers? Explain or show your reasoning.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Lin says, “When you add or multiply two complex numbers, you will always get an answer you can write in \(a+bi\) form.”

Noah says, “I don’t think so. Here are some exceptions I found:”

\((7+2i) + (-3-2i) = 10\)

\((2+2i)(2+2i) = 8i\)

1. Check Noah’s arithmetic. Is it correct?
2. Can Noah’s answers be written in the form \(a\), where \(b\) and \( \) are real numbers? Explain or show your reasoning.

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