Campbell Tyler
06/25/2023 · High School
Which of the following is \( |5-12 i| \) ?
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Tutor-Verified Answer
Step-by-step Solution
To find the magnitude of the complex number \( 5 - 12i \), we use the formula for the magnitude of a complex number \( a + bi \), which is given by:
\[
|a + bi| = \sqrt{a^2 + b^2}
\]
In this case, \( a = 5 \) and \( b = -12 \). Therefore, we can calculate the magnitude as follows:
\[
|5 - 12i| = \sqrt{5^2 + (-12)^2}
\]
Calculating \( 5^2 \) and \( (-12)^2 \):
\[
5^2 = 25
\]
\[
(-12)^2 = 144
\]
Now, we add these two results:
\[
25 + 144 = 169
\]
Finally, we take the square root:
\[
|5 - 12i| = \sqrt{169} = 13
\]
Thus, the magnitude \( |5 - 12i| \) is \( \boxed{13} \).
Quick Answer
The magnitude of \( |5 - 12i| \) is 13.
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