Problem

Given a complex number \( z = 5 + 3i \), find the magnitude and argument of \( z \).

Answer

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Answer

Step 2: Calculate the argument of \( z \) using the formula \( arg(z) = \arctan\left(\frac{b}{a}\right) \). So, \( arg(z) = \arctan\left(\frac{3}{5}\right) \)

Steps

Step 1 ：Step 1: Calculate the magnitude of \( z \) using the formula \( |z| = \sqrt{a^2 + b^2} \) where \( a \) is the real part and \( b \) is the imaginary part of \( z \). So, \( |z| = \sqrt{5^2 + 3^2} \)

Step 2 ：Step 2: Calculate the argument of \( z \) using the formula \( arg(z) = \arctan\left(\frac{b}{a}\right) \). So, \( arg(z) = \arctan\left(\frac{3}{5}\right) \)

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