Question 595437
Hi, there--

Remember that the letter i represents the complex number, the square root of -1. You solve this problem by using the distributive property. We have a two-term expression multiplied by another two-term expression. If you remember "FOIL" from earlier algebra classes, this is a similar process.
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Multiply each term in the first expression by each of the terms in the second expression. You will then have one 4-term expression.
{{{(sqrt(6)-i)(sqrt(6)+8i)}}}
{{{(sqrt(6))(sqrt(6))+(sqrt(6))(8i)+(-i)(sqrt(6))+(-i)(8i)}}}
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Now simplify and combine any like terms [Note:(-i)(i)=1].
{{{sqrt(36)+(sqrt(6))(8i)-(i)(sqrt(6))+(1)(8)}}}
{{{6+(sqrt(6))(8i)-(i)(sqrt(6))+8}}}
{{{(sqrt(6))(8i)-(i)(sqrt(6))+14}}}
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Now you can factor sqrt(6) out of the first two terms, and simplify.
{{{(sqrt(6))(8i-i)+14}}}
{{{(sqrt(6))(7i)+14}}}
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Hope this helps! Please email me if you are confused about any of my steps.
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Mrs. Figgy
math.in.the.vortex@gmail.com