SOLUTION: Find the sum, difference, product and qoutient of (2+3i) and (3-2i)

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Question 173647: Find the sum, difference, product and qoutient of (2+3i) and (3-2i)
Answer by jojo14344(1513)   (Show Source): You can put this solution on YOUR website!
SUM:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (2+3i)+(3-2i) simplifies to i+5
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (2+3i)+(3-2i) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around terms highlight_red%28+2+%29,highlight_red%28+3%2Ai+%29
It becomes .
Look at .
Remove unneeded parentheses around terms highlight_red%28+3+%29,highlight_red%28+-2%2Ai+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Moved 5 to the right of expression
It becomes .
Look at .
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 .
Look at .
Remove extraneous '1' from product highlight_red%28+%283-2%29+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!

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


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (2+3i)-(3-2i) simplifies to 5*i-1
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (2+3i)-(3-2i) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around terms highlight_red%28+2+%29,highlight_red%28+3%2Ai+%29
It becomes .
Look at .
Remove unneeded parentheses around terms highlight_red%28+-3+%29,highlight_red%28+2%2Ai+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Moved -1 to the right of expression
It becomes .
Look at .
Removed extra sign in front of -1
It becomes .
Look at .
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 .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!

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


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (2+3i)*(3-2i) simplifies to -6*i^2+5*i+6
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (2+3i)*(3-2i) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved 2 to the right of expression
It becomes .
Look at .
Moved 3 to the right of expression
It becomes .
Look at .
Expanded term %28-2%2Ai%2B3%29 by using associative property on %283%2Ai%2B2%29
It becomes .
Look at .
Expanded term 3%2Ai by using associative property on %28-2%2Ai%2B3%29
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Reduce similar several occurrences of highlight_red%28+i+%29 to highlight_green%28+i%5E2+%29
It becomes .
Look at .
Expanded term 2 by using associative property on %28-2%2Ai%2B3%29
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
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 .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!

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


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: (2+3i)/(3-2i) simplifies to (3*i+2)/(-2*i+3)
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (2+3i)/(3-2i) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved 2 to the right of expression
It becomes .
Look at .
Moved 3 to the right of expression
It becomes .
Result:

Universal Simplifier and Solver


Done!

thank you,
Jojo
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