Question

Help with imaginary numbers please!!!

Answer 1

Problem 1

Answer:  -7 + 8i

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Work Shown:

$-\sqrt{49}+\sqrt{-64}\\\\-\sqrt{7^2}+\sqrt{-1*8^2}\\\\-\sqrt{7^2}+\sqrt{-1}*\sqrt{8^2}\\\\-7+i*8\\\\-7+8i$

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Problem 2

Answer:   -2sqrt(6) + 10i

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Work Shown:

$\sqrt{-100}-\sqrt{24}\\\\\sqrt{-1*10^2}-\sqrt{4*6}\\\\\sqrt{-1*10^2}-\sqrt{2^2*6}\\\\\sqrt{-1}*\sqrt{10^2}-\sqrt{2^2}*\sqrt{6}\\\\i*10-2*\sqrt{6}\\\\-2\sqrt{6}+10i$

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Problem 3

Answer:   4 - 9i

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Work Shown:

$-\sqrt{-81}+\sqrt{16}\\\\-\sqrt{-1*9^2}+\sqrt{4^2}\\\\-\sqrt{-1}*\sqrt{9^2}+\sqrt{4^2}\\\\-i*9+4\\\\4-9i$

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Problem 4

Answer:   8i

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Work Shown:

$\sqrt{-1}*2\sqrt{16}\\\\\sqrt{-1}*2\sqrt{4^2}\\\\i*2*4\\\\8i$

We could express this as 0+8i, but I think 8i looks much cleaner.