Problem

Find the magnitude of the complex number \(z = 3 + 4i\)

Answer

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Answer

Step 3: Substitute \(a = 3\) and \(b = 4\) into the formula. So, the magnitude of the complex number is \(\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25}\).

Steps

Step 1 ：Step 1: Recall the formula of the magnitude of a complex number, which is given by \(\sqrt{a^2 + b^2}\), where \(a\) is the real part, and \(b\) is the imaginary part of the complex number.

Step 2 ：Step 2: In the given complex number \(z = 3 + 4i\), the real part \(a = 3\), and the imaginary part \(b = 4\).

Step 3 ：Step 3: Substitute \(a = 3\) and \(b = 4\) into the formula. So, the magnitude of the complex number is \(\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25}\).

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