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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-88}$

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Introduction to complex numbers

Full solution

Q. Use the imaginary number

i

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

-\sqrt{-88}

Breakdown of expression: First, let's break $-\sqrt{-88}$ into $-\sqrt{-1 \times 88}$ .
Use of imaginary unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ , so we can write $-\sqrt{-1 \times 88}$ as $-i \times \sqrt{88}$ .
Simplify $\sqrt{88}$ : Next, we simplify $\sqrt{88}$ by finding the prime factors of $88$ , which are $2$ , $2$ , $2$ , and $11$ . So, $\sqrt{88}$ is $\sqrt{2^3 \times 11}$ .
Factorize $\sqrt{88}$ : We can take out a pair of $2$ s from under the radical as a single $2$ , so $\sqrt{2^3 \times 11}$ becomes $2 \times \sqrt{2 \times 11}$ .
Final simplification: Now we have $-i \times 2 \times \sqrt{2 \times 11}$ , which simplifies to $-2i \times \sqrt{22}$ .

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