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This printable supports Common Core Mathematics Standard HSN-CN.A.3

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# Moduli of Complex Numbers (Grades 11-12)

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## Moduli of Complex Numbers

1.
What is the modulus of $-4 + 7i ?$
1. $65$
2. $sqrt(65)$
3. $33$
4. $-3$
2.
Given $z = 8 - 2i$, find $|z|$.
1. $2 sqrt(17)$
2. $2 sqrt(15)$
3. $68$
4. $60$
3.
Find the modulus of $-3i$.
1. $-3$
2. $sqrt(3)$
3. $sqrt(-3)$
4. $3$
4.
If $z$ is a complex number, and $|z| = 5$, which of the following are possible values of $z ?$ Choose all correct answers.
1. $z = 4 + i$
2. $z = 3 - 4i$
3. $z = 10 - 5i$
4. $z = 4 + 3i$
5.
Which of the following are possible values of $z$, a complex number, if $|z| = sqrt(13) ?$ Choose all correct answers.
1. $z = 2 - 3i$
2. $z = -3 - 2i$
3. $z = 2 + 3i$
4. $z = 2sqrt(3) + i$
6.
For $z in CC$, prove that $|z|^2 = z bar{z}$.

7.
For $z in CC$, prove that $|z| = | -z|$.

8.
For $z in CC$, prove that $|z| = o <=> z = 0$.

9.
For $z_1, z_2 in CC$, prove that $|z_1 z_2| = |z_1| |z_2|$.

10.
For $z_1, z_2 in CC$ and $z_2!=0$, prove that $|z_1/z_2| = |z_1| / |z_2|$.

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