anonymous
  • anonymous
evaluate the radical expression and express the result in a+bi form
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[(3-\sqrt{-5}) (1+\sqrt{-1})\]
campbell_st
  • campbell_st
well you need to distribute so it is \[3(1 + \sqrt{-1})-\sqrt{-5}(1 + \sqrt{-1})\] what do you think the next line of working is..?
anonymous
  • anonymous
\[3(1+i)-i \sqrt{5}(1+i)\]

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anonymous
  • anonymous
?
UnkleRhaukus
  • UnkleRhaukus
good, now distribute the 3, and the -i√5
anonymous
  • anonymous
\[(3+3i)(-i \sqrt{5}+1\sqrt{5}) ?\]
UsukiDoll
  • UsukiDoll
\[(3-\sqrt{-5}) (1+\sqrt{-1}) \] \[(3-\sqrt{5}i) (1+i)\] now expand.
UsukiDoll
  • UsukiDoll
all negatives in the radical should be pulled out first.. so that square root of -5 should be square root of 5 i
UnkleRhaukus
  • UnkleRhaukus
\[3(1+i)-i \sqrt{5}(1+i)\\=(3+3i)+(-i \sqrt{5}-\sqrt{5}i\times i) \]
UsukiDoll
  • UsukiDoll
\[(3-\sqrt{5}i) (1+i) \] \[3+3i-\sqrt{5}i-\sqrt{5}(i)(i)\] note \[i^2 = -1 \]
UsukiDoll
  • UsukiDoll
typed too fast... -1 inside the square root is just an i
anonymous
  • anonymous
\[(3+\sqrt{5})+(3-\sqrt{5})i\]
anonymous
  • anonymous
is that right?
UsukiDoll
  • UsukiDoll
hold on.
UsukiDoll
  • UsukiDoll
\[3+3i-\sqrt{5}i-\sqrt{5}(-1)\] \[3+3i-\sqrt{5}i+\sqrt{5}\] \[3+\sqrt{5}+3i-\sqrt{5}i\] \[\[3+\sqrt{5}+i(3-\sqrt{5})\]\] yeah it's correct
UsukiDoll
  • UsukiDoll
my i is placed differently, but it shouldn't matter because we still have a+bi only our a =\[3+\sqrt{5}\] and b = \[3-\sqrt{5}\]
anonymous
  • anonymous
thank you so much!
UsukiDoll
  • UsukiDoll
it's best to convert all negatives in the square root to i's first and if it's a perfect square like \[\sqrt{-1} \] just take the square root and add an i \[\sqrt{-1} \rightarrow i \] similarly for \[\sqrt{-5} \rightarrow \sqrt{5}i\]
UsukiDoll
  • UsukiDoll
but 5 isn't a perfect square so leave it in the radical and only the negative pops out of the radical and becomes i
UsukiDoll
  • UsukiDoll
negatives inside the radical produce imaginary results.
UsukiDoll
  • UsukiDoll
then use foil and i^2 = -1 ... simplify until a+bi or ai+b form is achieved.

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