Question

Help with imaginary numbers please!!!

Answer 1

Problem 1

Answer: -7 + 8i

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Work Shown:

`-√(49)+√(-64)\\\\-√(7^2)+√(-1*8^2)\\\\-√(7^2)+√(-1)*√(8^2)\\\\-7+i*8\\\\-7+8i\\\\`

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Problem 2

Answer: -2sqrt(6) + 10i

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Work Shown:

`√(-100)-√(24)\\\\√(-1*10^2)-√(4*6)\\\\√(-1*10^2)-√(2^2*6)\\\\√(-1)*√(10^2)-√(2^2)*√(6)\\\\i*10-2*√(6)\\\\-2√(6)+10i\\\\`

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Problem 3

Answer: 4 - 9i

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Work Shown:

`-√(-81)+√(16)\\\\-√(-1*9^2)+√(4^2)\\\\-√(-1)*√(9^2)+√(4^2)\\\\-i*9+4\\\\4-9i\\\\`

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Problem 4

Answer: 8i

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Work Shown:

`√(-1)*2√(16)\\\\√(-1)*2√(4^2)\\\\i*2*4\\\\8i\\\\`

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