(1)/((i^27)(- $\sqrt{3}$+5i))
You asked:
Evaluate the expression: \(\frac{1}{{i}^{27} \cdot \left(-\sqrt{3} + 5 i\right)}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{1}{{i}^{27} \cdot \left(-\sqrt{3} + 5 i\right)} = \frac{i}{- \sqrt{3} + 5 i} \)
Expanded
\[\frac{1}{{i}^{27} \cdot \left(-\sqrt{3} + 5 i\right)} = \frac{1}{5 + \sqrt{3} i}\]
Factored
\[\frac{1}{{i}^{27} \cdot \left(-\sqrt{3} + 5 i\right)} = - \frac{i}{\sqrt{3} - 5 i}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).