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To calculate the amplitude (or magnitude) of a complex number, you can use the following formula:

Amplitude = sqrt(Real^2 + Imaginary^2)

Here's a step-by-step guide to calculating the amplitude:

  1. Consider a complex number in the form z = a + bi, where "a" represents the real part and "b" represents the imaginary part.

  2. Square the real part and the imaginary part separately. In other words, calculate a^2 and b^2.

  3. Add the squared values from step 2. You'll have a^2 + b^2.

  4. Take the square root of the result obtained in step 3. This gives you the amplitude of the complex number.

Let's look at an example:

Consider the complex number z = 3 + 4i.

Step 1: The real part is a = 3, and the imaginary part is b = 4.

Step 2: Square the real and imaginary parts: a^2 = 3^2 = 9 and b^2 = 4^2 = 16.

Step 3: Add the squared values: 9 + 16 = 25.

Step 4: Take the square root of 25: sqrt(25) = 5.

Therefore, the amplitude (or magnitude) of the complex number 3 + 4i is 5.

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