Question

What is the value of (-√(-1)^ 8n+1+ (-√(-1)^ 8n+3 where n is a natural number?

Answer 1

Answer on Question #60708 – Math – Complex Analysis

Question

What is the value of $(-V(-1)^\wedge 8n+1 + (-V(-1)^\wedge 8n+3)$ where $n$ is a natural number?

Solution

$$\begin{array}{l} - \sqrt{(-1)}^{8n+1} + \sqrt{(-1)}^{8n+3} = -i^{8n+1} + i^{8n+3} = i^{8n}(i^3 - i) = \\ = (i^2 i^2)^{2n}(i \cdot i^2 - i) = (-1 \cdot (-1))^{2n}(i \cdot (-1) - i) = 1(-i - i) = -2i, \end{array}$$

where $i^2 = -1$.

**Answer**: -2i.

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