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11 grade maths others

How do you find the absolute value of 3 + 4i?

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9 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer9 Months ago

To find the absolute value of a complex number, such as \(3 + 4i\), you can use the formula:

Formula for Absolute Value

The absolute value (or modulus) of a complex number \(a + bi\) is calculated using:

|a + bi| = √(a² + b²)

Applying the Formula

In this case, \(a = 3\) and \(b = 4\). Plugging these values into the formula gives:

  • Calculate \(a²\): \(3² = 9\)
  • Calculate \(b²\): \(4² = 16\)
  • Add them together: \(9 + 16 = 25\)
  • Take the square root: \(\sqrt{25} = 5\)

Final Result

The absolute value of \(3 + 4i\) is 5.

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