Evaluate the expression $ \frac{4 + \sqrt{-9}}{2 + \sqrt{-1}} $ and write the result in the form \( a +...

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Evaluate the expression $ \frac{4 + \sqrt{-9}}{2 + \sqrt{-1}} $ and write the result in the form $ a + bi $. The real number a equals The real number b equals

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To evaluate $ \frac{4 + \sqrt{-9}}{2 + \sqrt{-1}} $, we first simplify the expression:$ \sqrt{-9} = 3i $ and $ \sqrt{-1} = i $.So the expression becomes $ \frac{4 + 3i}{2 + i} $.Multiply the numerator and denominator by the conjugate of the denominator:$ \frac{(4 + 3i)(2 - i)}{(2 + i)(2 - i)} $.The denominator simplifies to $ 4 + 1 = 5 $.The numerator simplifies as follows:$ (4 + 3i)(2 - i) = 8 - 4i + 6i - 3i^2 = 8 + 2i + 3 = 11 + 2i $.Thus, the expression becomes $ \frac{11 + 2i}{5} = \frac{11}{5} + \frac{2}{5}i $. a equals $ \frac{11}{5} $. b equals $ \frac{2}{5} $.

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Evaluate the expression \( \frac{4 + \sqrt{-9}}{2 + \sqrt{-1}} \) and write the result in the form \( a +...

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