SOLUTION: Simplify the following expression and express your final answer in rectangular form. {{{ (2+3j)/(5-4j) }}} Confused on how to go about solving this question, also what do the

Algebra ->  Functions -> SOLUTION: Simplify the following expression and express your final answer in rectangular form. {{{ (2+3j)/(5-4j) }}} Confused on how to go about solving this question, also what do the      Log On


   

Question 949995: Simplify the following expression and express your final answer in rectangular form.
+%282%2B3j%29%2F%285-4j%29+
Confused on how to go about solving this question, also what do they mean rectangular form?
Thank you
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

to simplify +%282%2B3j%29%2F%285-4j%29+ first get rid of j in denominator

+%282%2B3j%29%2F%285-4j%29+....multiply both numerator and denominator by %285%2B4j%29(why?; recall the "difference of squares" formula we can use it here)
+%28%282%2B3j%29%285%2B4j%29%29%2F%28%285%2B4j%29%285-4j%29%29+....now, multiply terms in numerator and write your denominator as the difference of the squares
+%28%2810%2B8j%2B15j%2B3%2A4%2Aj%5E2%29%29%2F%285%5E2-%284j%29%5E2%29+
+%2810%2B23j%2B12%2A%28-1%29%29%2F%2825-%2816%28-1%29%29%29+
+%28-2%2B23j%29%2F%2825%2B16%29+
+%28-2%2B23j%29%2F41+
+-2%2F41%2B23j%2F41+
as decimal
0.048780487804878+%2B++0.5609756097560976j ...round it to two decimal places
0.05+%2B++0.56j

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
The numerator and denominator represent complex numbers
we are given (2+3j) / (5-4j), then
first multiply the conjugate of the denominator by the denominator and numerator
conjugate of denominator is (5+4j), therefore
(2+3j) / (5-4j) * (5+4j) / (5+4j) = (23j-2) / 41 = (-2 +23j)/41 = -2/41 +23j/41
note that j^2 = -1
therefore we have -2/41 + 23j/41
complex number uses rectangular form (rectangular coordinate system) in the following manner
the real portion in our problem is -2/41 is represented on the x axis and 23j/41 is represented on the y axis by 23/41 and the rectangular coordinate point is
(-2/41, 23/41)
note that rectangular form is -2/41 + 23j/41