I'm kinda confused with this problem. We're working with imaginary numbers. Is my work correct?
Compare the quantity in Column A with the quantity in Column B.
Column A = |3 - 2i|
Column B = |5 - i|
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My work
Column A
3 + 2 = 5
Column B
5 + 1= 6
Answer: Column B is greater.
Clearly you have not read the section on complex numbers
|3-2i| = √(3^2+2^2) = √13
|5-i| = √(5^2+1^2) = √26
I actually did, but my textbook and study guide didn't have any practice questions like this one. Thanks for your help anyways. Have a nice day!
pardon my skepticism. Any introduction to complex numbers explains how to find their magnitude.
To compare the quantities in Column A and Column B correctly, you need to calculate the magnitudes of the imaginary numbers involved.
First, let's find the magnitude of the quantity in Column A, which is |3 - 2i|.
To calculate the magnitude of a complex number, you use the formula:
|a + bi| = √(a² + b²),
where a and b are the real and imaginary parts, respectively.
In this case, a = 3 and b = -2. Let's calculate it:
|3 - 2i| = √(3² + (-2)²) = √(9 + 4) = √13.
So, the magnitude of the quantity in Column A is √13.
Now, let's find the magnitude of the quantity in Column B, which is |5 - i|.
In this case, a = 5 and b = -1. Calculating it:
|5 - i| = √(5² + (-1)²) = √(25 + 1) = √26.
So, the magnitude of the quantity in Column B is √26.
Now, we can compare the magnitudes:
√13 versus √26
Since √26 is greater than √13, the correct answer is:
Column B is greater.
Therefore, your initial work is incorrect, and you should revise it based on the correct magnitude calculations.