Problem preview

N-CN.8 Warmup M2-058-A07-V03

Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.

Decide whether a proposed algebraic identity is true for complex numbers

Problem

Is this identity true for complex numbers? \((z+i)(z-i)=z^2+1\)

Answer choices

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No, because (z+i)(z-i) = z² - i² = z² - 1, so it does not equal z² + 1.

Yes, because the middle terms cancel and leave z² − 1.

Yes, because (z+i)(z-i) = z² - i² = z² - (-1) = z² + 1.

No, because (z + i)(z − i) = z² − 1.

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Curriculum context

Course: Math II
Standard: N-CN.8
Category: Number and Quantity
Domain: The Complex Number System
Objective: Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.
Problem type: Decide whether a proposed algebraic identity is true for complex numbers