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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-77}$

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Introduction to complex numbers

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Q. Use the imaginary number

i

to rewrite the expression below as a complex number. Simplify all radicals.

\sqrt{-77}

Breakdown of $\sqrt{-77}$ : First, let's break down $\sqrt{-77}$ into $\sqrt{-1}$ and $\sqrt{77}$ . $\newline$ $\sqrt{-77} = \sqrt{-1 \times 77}$
Use of imaginary unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ . So, $\sqrt{-77} = i \times \sqrt{77}$
Simplify $\sqrt{77}$ : Next, we need to simplify $\sqrt{77}$ . Since $77$ is not a perfect square, we can't simplify it further. $\newline$ So, $\sqrt{-77} = i \cdot \sqrt{77}$
Check for perfect square factors: But wait, we made a mistake. We need to check if $77$ has any perfect square factors to simplify $\sqrt{77}$ . $77 = 7 \times 11$ , and neither $7$ nor $11$ is a perfect square. So, there's no simplification possible.

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