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.
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Information: IM Alg2.3.14 Lesson: More Arithmetic with Complex Numbers