SOLUTION: Express in simplest form, in terms of i. 2[SQRT(-81)] - 2[SQRT(-100)] Please help with this question, i have no idea where to start! thanks!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Express in simplest form, in terms of i. 2[SQRT(-81)] - 2[SQRT(-100)] Please help with this question, i have no idea where to start! thanks!      Log On


   

Question 1128382: Express in simplest form, in terms of i. 2[SQRT(-81)] - 2[SQRT(-100)]
Please help with this question, i have no idea where to start! thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use these rules
Rule 1: i+=+sqrt%28-1%29 by definition
Rule 2: sqrt%28x%2Ay%29+=+sqrt%28x%29%2Asqrt%28y%29
Rule 3: sqrt%28x%5E2%29+=+x where x is nonnegative

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2%2Asqrt%28-81%29+-+2%2Asqrt%28-100%29+=+2%2Asqrt%28-1%2A81%29+-+2%2Asqrt%28-1%2A100%29

Use rule 2



2%2Asqrt%28-81%29+-+2%2Asqrt%28-100%29+=+2%2Ai%2Asqrt%289%5E2%29+-+2%2Ai%2Asqrt%2810%5E2%29 Use rule 1

2%2Asqrt%28-81%29+-+2%2Asqrt%28-100%29+=+2%2Ai%2A9+-+2%2Ai%2A10 Use rule 3

2%2Asqrt%28-81%29+-+2%2Asqrt%28-100%29+=+18i+-+20i

2%2Asqrt%28-81%29+-+2%2Asqrt%28-100%29+=+-2i

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Answer: -2i