Question 41215: What is the answer of (3-2i)/(7-6i) in standard form. Thank you
Answer by zeynep(43)   (Show Source):
You can put this solution on YOUR website! To write (3-2i)/(7-6i) in standard form, we will make the denominator a real number.
To make the denominator a real number, we multiply it by its conjugate which is (7+6i).
However we will also multiply the numerator by (7+6i) in order not to change the fraction.(Keep in mind that as long as you multiply the numerator and denominator by the exact the same thing, the fractions will be equivalent.)
So,
(3-2i)/(7-6i)=(3-2i).(7+6i)/(7-6i).(7+6i)
Now let's do the multiplications;
(3-2i).(7+6i)=21+18i-14i-12i^2 = 21+4i-12.(-1)(Here we used that i^2=-1)
21+4i-12.(-1)=21+4i+12=33+4i (This is the numerator)
Now let's find the denominator;
When you multiply comlex conjugates together you get:
(a-bi)(a+bi)=a^2+b^2
so,
(7-6i).(7+6i)= 7^2+6^2= 49+36=85 (This is the denominator)
So the standard from of (3-2i)/(7-6i) is;
(3-2i)/(7-6i)=(3-2i).(7+6i)/(7-6i).(7+6i)= 33+4i /85
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