To find the absolute value of a complex number, we use the formula:
|z| = √(a² + b²)
where z = a + bi, with a representing the real part and b the imaginary part of the complex number.
In this case, for the complex number z = 3 + 4i, we have:
- a = 3
- b = 4
Now plug these values into the formula:
|z| = √(3² + 4²)
This simplifies to:
|z| = √(9 + 16)
|z| = √25
|z| = 5
Therefore, the absolute value of the complex number 3 + 4i is 5.