- Identify the denominator \(\frac{-5}{2 - 0i}\) as the real number 2.
- Rewrite the expression as the simple division \(\frac{-5}{2}\).
- Calculate the final value, resulting in \(\boxed{-2.5}\).
Explanation
- Simplifying the denominator
The expression given is \(\frac{-5}{2 - 0i}\). To simplify this, we first examine the denominator, which is a complex number in the form \(a + bi\), where \(a = 2\) and \(b = 0\). A complex number where the imaginary part is zero is equivalent to its real part. Therefore, \(2 - 0i = 2\).
- Performing the division
Having simplified the denominator to \(2\), the entire expression becomes a simple division of two real numbers: \(\frac{-5}{2}\). Dividing \(-5\) by \(2\) gives \(-2.5\). Thus, the result of the division is \(-2.5\).
Examples
In engineering or physics, you might encounter scenarios where you calculate ratios of forces or velocities that are initially expressed using complex notation, but reduce to simple real values because the imaginary components vanish. For instance, if a force vector component in the imaginary direction is zero, it means the force acts entirely along the real axis, simplifying calculations such as determining the scaling factor for that force. Dividing real values is a fundamental operation in scaling and normalization tasks across many technical fields.