The absolute value (or modulus) of a complex number is a measure of its distance from the origin in the complex plane. For a complex number expressed in the form a + bi, where a is the real part and b is the imaginary part, the absolute value is calculated using the formula:
|z| = √(a² + b²)
In this case, the complex number is 4 + 2i, where a = 4 and b = 2.
Now, let’s plug these values into the formula:
- |4 + 2i| = √(4² + 2²)
- |4 + 2i| = √(16 + 4)
- |4 + 2i| = √20
- |4 + 2i| = √(4 × 5)
- |4 + 2i| = 2√5
Thus, the absolute value of the complex number 4 + 2i is 2√5, which is approximately 4.47.