document.write( "Question 173647: Find the sum, difference, product and qoutient of (2+3i) and (3-2i) \n" ); document.write( "
Algebra.Com's Answer #128524 by jojo14344(1513)\"\" \"About 
You can put this solution on YOUR website!
SUM:
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • Graphical form: \"%282%2B3i%29%2B%283-2i%29\" simplifies to \"i%2B5\"
  • Text form: (2+3i)+(3-2i) simplifies to i+5
  • Cartoon (animation) form: \"simplify_cartoon%28+%282%2B3i%29%2B%283-2i%29+%29\"
    For tutors: simplify_cartoon( (2+3i)+(3-2i) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+%282%2B3%2Ai%29+%29%2B%283-2%2Ai%29\".
Remove unneeded parentheses around terms \"highlight_red%28+2+%29\",\"highlight_red%28+3%2Ai+%29\"
It becomes \"highlight_green%28+2+%29%2Bhighlight_green%28+3%2Ai+%29%2B%283-2%2Ai%29\".
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Look at \"2%2B3%2Ai%2Bhighlight_red%28+%283-2%2Ai%29+%29\".
Remove unneeded parentheses around terms \"highlight_red%28+3+%29\",\"highlight_red%28+-2%2Ai+%29\"
It becomes \"2%2B3%2Ai%2Bhighlight_green%28+3+%29-highlight_green%28+2%2Ai+%29\".
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Look at \"highlight_red%28+2+%29%2B3%2Ai%2Bhighlight_red%28+3+%29-2%2Ai\".
Added fractions or integers together
It becomes \"highlight_green%28+5+%29%2B3%2Ai-2%2Ai\".
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Look at \"highlight_red%28+5+%29%2B3%2Ai-2%2Ai\".
Moved \"5\" to the right of expression
It becomes \"3%2Ai-2%2Ai%2Bhighlight_green%28+5+%29\".
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Look at \"highlight_red%28+3%2Ai+%29-highlight_red%28+2%2Ai+%29%2B5\".
Eliminated similar terms \"highlight_red%28+3%2Ai+%29\",\"highlight_red%28+-2%2Ai+%29\" replacing them with \"highlight_green%28+%283-2%29%2Ai+%29\"
It becomes \"highlight_green%28+%283-2%29%2Ai+%29%2B5\".
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Look at \"highlight_red%28+%283-2%29+%29%2Ai%2B5\".
Remove extraneous '1' from product \"highlight_red%28+%283-2%29+%29\"
It becomes \"i%2B5\".
Result: \"i%2B5\"
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Universal Simplifier and Solver

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Done!

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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


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  • Graphical form: \"%282%2B3i%29-%283-2i%29\" simplifies to \"5%2Ai-1\"
  • Text form: (2+3i)-(3-2i) simplifies to 5*i-1
  • Cartoon (animation) form: \"simplify_cartoon%28+%282%2B3i%29-%283-2i%29+%29\"
    For tutors: simplify_cartoon( (2+3i)-(3-2i) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+%282%2B3%2Ai%29+%29-%283-2%2Ai%29\".
Remove unneeded parentheses around terms \"highlight_red%28+2+%29\",\"highlight_red%28+3%2Ai+%29\"
It becomes \"highlight_green%28+2+%29%2Bhighlight_green%28+3%2Ai+%29-%283-2%2Ai%29\".
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Look at \"2%2B3%2Ai-highlight_red%28+%283-2%2Ai%29+%29\".
Remove unneeded parentheses around terms \"highlight_red%28+-3+%29\",\"highlight_red%28+2%2Ai+%29\"
It becomes \"2%2B3%2Ai-highlight_green%28+3+%29%2Bhighlight_green%28+2%2Ai+%29\".
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Look at \"highlight_red%28+2+%29%2B3%2Ai-highlight_red%28+3+%29%2B2%2Ai\".
Added fractions or integers together
It becomes \"highlight_green%28+-1+%29%2B3%2Ai%2B2%2Ai\".
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Look at \"highlight_red%28+-1+%29%2B3%2Ai%2B2%2Ai\".
Moved \"-1\" to the right of expression
It becomes \"3%2Ai%2B2%2Ai%2Bhighlight_green%28+-1+%29\".
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Look at \"3%2Ai%2B2%2Ai%2Bhighlight_red%28+-1+%29\".
Removed extra sign in front of \"-1\"
It becomes \"3%2Ai%2B2%2Ai-highlight_green%28+1+%29\".
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Look at \"highlight_red%28+3%2Ai+%29%2Bhighlight_red%28+2%2Ai+%29-1\".
Eliminated similar terms \"highlight_red%28+3%2Ai+%29\",\"highlight_red%28+2%2Ai+%29\" replacing them with \"highlight_green%28+%283%2B2%29%2Ai+%29\"
It becomes \"highlight_green%28+%283%2B2%29%2Ai+%29-1\".
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Look at \"%28highlight_red%28+3+%29%2Bhighlight_red%28+2+%29%29%2Ai-1\".
Added fractions or integers together
It becomes \"%28highlight_green%28+5+%29%29%2Ai-1\".
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Look at \"highlight_red%28+%28highlight_red%28+5+%29%29%2Ai+%29-1\".
Remove unneeded parentheses around factor \"highlight_red%28+5+%29\"
It becomes \"highlight_green%28+5+%29%2Ai-1\".
Result: \"5%2Ai-1\"
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Universal Simplifier and Solver

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Done!

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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


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  • Graphical form: \"%282%2B3i%29%2A%283-2i%29\" simplifies to \"-6%2Ai%5E2%2B5%2Ai%2B6\"
  • Text form: (2+3i)*(3-2i) simplifies to -6*i^2+5*i+6
  • Cartoon (animation) form: \"simplify_cartoon%28+%282%2B3i%29%2A%283-2i%29+%29\"
    For tutors: simplify_cartoon( (2+3i)*(3-2i) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"%28highlight_red%28+2+%29%2B3%2Ai%29%2A%283-2%2Ai%29\".
Moved \"2\" to the right of expression
It becomes \"%283%2Ai%2Bhighlight_green%28+2+%29%29%2A%283-2%2Ai%29\".
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Look at \"%283%2Ai%2B2%29%2A%28highlight_red%28+3+%29-2%2Ai%29\".
Moved \"3\" to the right of expression
It becomes \"%283%2Ai%2B2%29%2A%28-2%2Ai%2Bhighlight_green%28+3+%29%29\".
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Look at \"highlight_red%28+%283%2Ai%2B2%29%2A%28-2%2Ai%2B3%29+%29\".
Expanded term \"%28-2%2Ai%2B3%29\" by using associative property on \"%283%2Ai%2B2%29\"
It becomes .
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Look at \"highlight_red%28+%28-2%2Ai%2B3%29%2A3%2Ai+%29%2B%28-2%2Ai%2B3%29%2A2\".
Expanded term \"3%2Ai\" by using associative property on \"%28-2%2Ai%2B3%29\"
It becomes .
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Look at \"-highlight_red%28+3+%29%2Ai%2Ahighlight_red%28+2+%29%2Ai%2B3%2Ai%2A3%2B%28-2%2Ai%2B3%29%2A2\".
Multiplied numerator integers
It becomes \"-highlight_green%28+6+%29%2Ai%2Ai%2B3%2Ai%2A3%2B%28-2%2Ai%2B3%29%2A2\".
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Look at \"-6%2Ai%2Ai%2Bhighlight_red%28+3+%29%2Ai%2Ahighlight_red%28+3+%29%2B%28-2%2Ai%2B3%29%2A2\".
Multiplied numerator integers
It becomes \"-6%2Ai%2Ai%2Bhighlight_green%28+9+%29%2Ai%2B%28-2%2Ai%2B3%29%2A2\".
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Look at \"-6%2Ahighlight_red%28+i+%29%2Ahighlight_red%28+i+%29%2B9%2Ai%2B%28-2%2Ai%2B3%29%2A2\".
Reduce similar several occurrences of \"highlight_red%28+i+%29\" to \"highlight_green%28+i%5E2+%29\"
It becomes \"-6%2Ahighlight_green%28+i%5E2+%29%2B9%2Ai%2B%28-2%2Ai%2B3%29%2A2\".
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Look at \"-6%2Ai%5E2%2B9%2Ai%2Bhighlight_red%28+%28-2%2Ai%2B3%29%2A2+%29\".
Expanded term \"2\" by using associative property on \"%28-2%2Ai%2B3%29\"
It becomes \"-6%2Ai%5E2%2B9%2Ai-highlight_green%28+2%2A2%2Ai+%29%2Bhighlight_green%28+2%2A3+%29\".
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Look at \"-6%2Ai%5E2%2B9%2Ai-highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2Ai%2B2%2A3\".
Multiplied numerator integers
It becomes \"-6%2Ai%5E2%2B9%2Ai-highlight_green%28+4+%29%2Ai%2B2%2A3\".
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Look at \"-6%2Ai%5E2%2B9%2Ai-4%2Ai%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+3+%29\".
Multiplied numerator integers
It becomes \"-6%2Ai%5E2%2B9%2Ai-4%2Ai%2Bhighlight_green%28+6+%29\".
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Look at \"-6%2Ai%5E2%2Bhighlight_red%28+9%2Ai+%29-highlight_red%28+4%2Ai+%29%2B6\".
Eliminated similar terms \"highlight_red%28+9%2Ai+%29\",\"highlight_red%28+-4%2Ai+%29\" replacing them with \"highlight_green%28+%289-4%29%2Ai+%29\"
It becomes \"-6%2Ai%5E2%2Bhighlight_green%28+%289-4%29%2Ai+%29%2B6\".
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Look at \"-6%2Ai%5E2%2B%28highlight_red%28+9+%29-highlight_red%28+4+%29%29%2Ai%2B6\".
Added fractions or integers together
It becomes \"-6%2Ai%5E2%2B%28highlight_green%28+5+%29%29%2Ai%2B6\".
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Look at \"-6%2Ai%5E2%2Bhighlight_red%28+%28highlight_red%28+5+%29%29%2Ai+%29%2B6\".
Remove unneeded parentheses around factor \"highlight_red%28+5+%29\"
It becomes \"-6%2Ai%5E2%2Bhighlight_green%28+5+%29%2Ai%2B6\".
Result: \"-6%2Ai%5E2%2B5%2Ai%2B6\"
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Universal Simplifier and Solver

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Done!

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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


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    \n" ); document.write( "
  • Graphical form: \"%282%2B3i%29%2F%283-2i%29\" simplifies to \"%283%2Ai%2B2%29%2F%28-2%2Ai%2B3%29\"
  • Text form: (2+3i)/(3-2i) simplifies to (3*i+2)/(-2*i+3)
  • Cartoon (animation) form: \"simplify_cartoon%28+%282%2B3i%29%2F%283-2i%29+%29\"
    For tutors: simplify_cartoon( (2+3i)/(3-2i) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"%28highlight_red%28+2+%29%2B3%2Ai%29%2F%283-2%2Ai%29\".
Moved \"2\" to the right of expression
It becomes \"%283%2Ai%2Bhighlight_green%28+2+%29%29%2F%283-2%2Ai%29\".
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Look at \"%283%2Ai%2B2%29%2F%28highlight_red%28+3+%29-2%2Ai%29\".
Moved \"3\" to the right of expression
It becomes \"%283%2Ai%2B2%29%2F%28-2%2Ai%2Bhighlight_green%28+3+%29%29\".
Result: \"%283%2Ai%2B2%29%2F%28-2%2Ai%2B3%29\"
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Universal Simplifier and Solver

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Done!

\n" ); document.write( "\n" ); document.write( "thank you,
\n" ); document.write( "Jojo \n" ); document.write( "
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