Question

What is the absolute value of the number?
3 + i? Please help.

Answer 1

To take the absolute value of a complex number such as 3 + i, you need to compute its magnitude.

Consider a complex number (a + bi) where i^2 = -1. The magnitude is the hypotenuse of a right triangle with sides of length a and b. Because we are taking the absolute value, we will always use the positive square root. We find the hypotenuse by the Pythagorean theorem.

\[|a + bi| = +\sqrt{a^2 + b^2}\]

For |3+i|, a = 3, b = 1. Plug in the numbers and do the arithmetic...