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

Algebra ->  Equations -> SOLUTION: Find the sum, difference, product and qoutient of (2+3i) and (3-2i)      Log On


   

Question 173647: Find the sum, difference, product and qoutient of (2+3i) and (3-2i)
Answer by jojo14344(1513) About Me  (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: %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) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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

Universal Simplifier and Solver


Done!

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


YOUR ANSWER


  • 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) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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

Universal Simplifier and Solver


Done!

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


YOUR ANSWER


  • 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) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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 .
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 .
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.
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.
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.
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.
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.
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.
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.
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.
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

Universal Simplifier and Solver


Done!

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


YOUR ANSWER


  • 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) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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

Universal Simplifier and Solver


Done!

thank you,
Jojo