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Chapter 6: Problem 13

Evaluate \(|4-3 i|\).

Short Answer

Expert verified
The modulus of the complex number \(4 - 3i\) is calculated as \(|4 - 3i| = \sqrt{4^2 + (-3)^2} = \sqrt{25} = 5\).

Step by step solution

01

Identify the real and imaginary parts of the complex number

For the complex number 4 - 3i, the real part (a) is 4, and the imaginary part (b) is -3.
02

Calculate the square of the real and imaginary parts

Calculate the square of both the real and imaginary parts: \(a^2 = (4)^2 = 16\) \(b^2 = (-3)^2 = 9\)
03

Sum the squares of the real and imaginary parts

Add the squares of the real and imaginary parts together: \(a^2 + b^2 = 16 + 9 = 25\)
04

Calculate the square root of the sum

Take the square root of the sum we calculated in the previous step: \(|4 - 3i| = \sqrt{25} = 5\) So, the modulus of the complex number 4 - 3i is 5.

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