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Mathematics 19 Online
OpenStudy (omgthatgirl):

Help. Simplify the complex number 5+square root -54 and write it in correct notation

OpenStudy (bloomlocke367):

is it \[5+\sqrt {-54}?\]

OpenStudy (amorfide):

that is what she has yes

OpenStudy (bloomlocke367):

first, you need to take out the negative... and that looks like this:\[5+i \sqrt{54}\] because i is the same as \[\sqrt{-1}\]

OpenStudy (bloomlocke367):

@Omgthatgirl are you there?..

OpenStudy (omgthatgirl):

Yea ok got it thanks

OpenStudy (bloomlocke367):

then you need to figure out how to finish simplifying the radical... do you know how to do that?

OpenStudy (omgthatgirl):

yea it's 5+8i

OpenStudy (jdoe0001):

\(\bf 5+\sqrt{-54}\quad {\color{brown}{ 54\to 2\cdot 3\cdot 3\cdot 3\to 2\cdot 3\cdot 3^2 }} \\ \quad \\ 5+\sqrt{-54}\implies 5+\sqrt{-1\cdot 54}\implies 5+\sqrt{-1}\cdot \sqrt{54} \\ \quad \\ 5+\sqrt{-1}\cdot \sqrt{{\color{brown}{ 2\cdot 3\cdot 3^2 }}}\)

OpenStudy (bloomlocke367):

how is it 8?...

OpenStudy (omgthatgirl):

I don't know but that was the right answer

OpenStudy (bloomlocke367):

okayyyyyy did you was it really -54 or was it supposed to be -64?

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