(1)/((i^27)(- $\sqrt{3}$+5i))

asked by guest
on Oct 25, 2024 at 10:29 pm



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 \(i^2 = -1\).

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