SOLUTION: Perform the indicated operation.. {{{ (9-8i)+(7+2i) }}}. {{{ (3+4i)(2-6i) }}}. {{{ (6+3i)/(2+2i) }}}.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Perform the indicated operation.. {{{ (9-8i)+(7+2i) }}}. {{{ (3+4i)(2-6i) }}}. {{{ (6+3i)/(2+2i) }}}.      Log On


   

Question 151572: Perform the indicated operation..
+%289-8i%29%2B%287%2B2i%29+.
+%283%2B4i%29%282-6i%29+.
+%286%2B3i%29%2F%282%2B2i%29+.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+%289-8i%29%2B%287%2B2i%29+ Start with the given expression.


+%289%2B7%29%2B%28-8i%2B2i%29+ Group like terms


+16-6i+ Combine like terms

So %289-8i%29%2B%287%2B2i%29=16-6i

So the expression is in standard form a%2Bbi where a=16 and b=-6




%283%2B4i%29%282-6i%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%283%29%2B4i%29%28highlight%282%29-6i%29 Multiply the First terms:%283%29%2A%282%29=6.


%28highlight%283%29%2B4i%29%282%2Bhighlight%28-6i%29%29 Multiply the Outer terms:%283%29%2A%28-6%2Ai%29=-18%2Ai.


%283%2Bhighlight%284i%29%29%28highlight%282%29-6i%29 Multiply the Inner terms:%284%2Ai%29%2A%282%29=8%2Ai.


%283%2Bhighlight%284i%29%29%282%2Bhighlight%28-6i%29%29 Multiply the Last terms:%284%2Ai%29%2A%28-6%2Ai%29=-24%2Ai%5E2=-24%28-1%29=24.


6-18%2Ai%2B8%2Ai%2B24 Now collect every term to make a single expression.


30-10%2Ai Now combine like terms.


So %283%2B4i%29%282-6i%29 FOILS to 30-10%2Ai.


In other words, %283%2B4i%29%282-6i%29=30-10%2Ai.

So the expression is in standard form a%2Bbi where a=30 and b=-10







%286%2B3i%29%2F%282%2B2i%29 Start with the given expression


%28%286%2B3i%29%2F%282%2B2i%29%29%28%282-2i%29%2F%282-2i%29%29 Multiply by the fraction by %282-2i%29%2F%282-2i%29. Note 2-2i is the conjugate of 2%2B2i.


%28%286%2B3i%29%282-2i%29%29%2F%28%282%2B2i%29%282-2i%29%29 Combine the fractions


%28%286%2B3i%29%282-2i%29%29%2F%284%2B4i-4i-4i%5E2%29 Foil the denominator


%28%286%2B3i%29%282-2i%29%29%2F%284-4i%5E2%29 Combine like terms


%28%286%2B3i%29%282-2i%29%29%2F%284-4%28-1%29%29 Rewrite i%5E2 as -1


%28%286%2B3i%29%282-2i%29%29%2F%284%2B4%29 Multiply


%28%286%2B3i%29%282-2i%29%29%2F%288%29 Add


%2812-12i%2B6i-6i%5E2%29%2F%288%29 FOIL the numerator


%2812-12i%2B6i-6%28-1%29%29%2F%288%29 Rewrite i%5E2 as -1


%2812-12i%2B6i%2B6%29%2F%288%29 Multiply


%2818-6i%29%2F%288%29 Combine like terms.


%2818%29%2F%288%29-%286i%29%2F%288%29 Break up the fraction


%289%29%2F%284%29-%283%2F4%29i Reduce


So %286%2B3i%29%2F%282%2B2i%29=%289%29%2F%284%29-%283%2F4%29i.


So the expression is in standard form a%2Bbi where a=9%2F4 and b=3%2F4