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Chapter 2: Problem 30

Perform the indicated operations and write the result in standard form. $$\sqrt{-81}-\sqrt{-144}$$

Short Answer

Expert verified
The result of the operation \(\sqrt{-81} - \sqrt{-144}\) is \(-3i\).

Step by step solution

01

Identify the negative square roots

The square root of a negative number can be simplified by recognizing that \(\sqrt{-1} = i\). Thus, \(\sqrt{-a} = \sqrt{a}i\). In this case: \(\sqrt{-81} = \sqrt{81}i = 9i\) and \(\sqrt{-144} = \sqrt{144}i = 12i\).
02

Perform the operation

Now subtract the two complex numbers: \(9i - 12i\).
03

Write the result in standard form

Combine the 'like' terms. The result is \(-3i\) which is in standard form since \(a\) is 0.

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Most popular questions from this chapter

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{3 x-7}{x-2}$$

What is a rational function?

Find the horizontal asymptote, if there is one, of the graph of rational function. $$h(x)=\frac{15 x^{3}}{3 x^{2}+1}$$

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2}>0$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$g(x)=\frac{1}{x+2}-2$$
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