Question

simplify the expression to ( a + bi ) form:
( -sqrt{4} + sqrt{-72} + sqrt{64} - sqrt{-98} )

Explanation:

Step1: Simplify real square roots

$-\sqrt{4} = -2$, $\sqrt{64} = 8$

Step2: Simplify imaginary square roots

$\sqrt{-72} = \sqrt{72}i = 6\sqrt{2}i$, $\sqrt{-98} = \sqrt{98}i = 7\sqrt{2}i$

Step3: Combine real terms

$-2 + 8 = 6$

Step4: Combine imaginary terms

$6\sqrt{2}i - 7\sqrt{2}i = -\sqrt{2}i$

Step5: Combine real and imaginary parts

$6 + (-\sqrt{2}i)$

Answer:

$6 - \sqrt{2}i$