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What is the modulus of the complex number 𝑎 plus 𝑏𝑖, where 𝑎 and 𝑏 are real?
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If we consider the general complex number 𝑧 equals 𝑥 plus 𝑖𝑦 where 𝑥 and 𝑦 are real and 𝑖 is equal to the square root of negative one, then the square root of 𝑥 squared plus 𝑦 squared is the modulus or absolute value of 𝑧.
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This is denoted as shown.
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We find the sum of the squares of the real and imaginary parts of the number and then square root the answer.
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The real part of our complex number is equal to 𝑎, and the imaginary part is equal to 𝑏.
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This means that the modulus of the complex number 𝑎 plus 𝑏𝑖 is the square root of 𝑎 squared plus 𝑏 squared.