Question

Solve.

Answer 1

\[\frac{4+3i}{(7-2i)(5+4i)}\]

Answer 2

http://www.wolframalpha.com/input/?i=%284%2B3i%29%2F%28%287-2i%29*%285%2B4i%29%29

Answer 3

4+3i/(7-2i)(5+4i)
We multiply the 2 complex numbers:
And we get=
4+3i/18i + 43
From here, we can just rationalize the denominator so:
We get the final answer as:
-226-57i/-1867

Answer 4

we have
\[\frac{4+3i}{(7-2i)(5+4i)}\]
multiply numerator and denominator by the conjugate of (7-2i) and (5+4i), that is (7+2i) and (5-4i)
so we have
\[\frac{(4+3i)(7+2i)(5-4i)}{(7-2i)(7+2i)(5-4i)(5+4i)}\]
now (a+bi)(a-bi)=a^2+b^2
so
we have now
\[\frac{(4+3i)(7+2i)(5-4i)}{(7^2+2^2)(5^2+4^2)}\]
now let's simplify the numerator by multiplying and remembering that i^2=-1
\[\frac{(28+8i+21i+6i^2)(5-4i)}{(53)(41)}\]
we get now
\[\frac{(28+8i+21i-6)(5-4i)}{(53)(41)}\]
now we have
\[\frac{(22+29i)(5-4i)}{(53)(41)}\]
now multiply the other two brackets
\[\frac{(110-88i+145i-116i^2)}{(53)(41)}\]
now simplifying the terms and substituting i^2=-1
\[\frac{(110-116+57i)}{(53)(41)}\]
we get
\[\frac{(-6+57i)}{(53)(41)}\]
or
\[\frac{-6+57i}{2173}\]

Answer 5

Thanks man!!!!

Answer 6

sorry i made a mistake in the third last step
it'd be
\[\frac{110+116+57i}{53*41}\]
so it's
\[\frac{226+57i}{53*41}\]
finally we get
\[\frac{226+57i}{2173}\]
sorry I made a mistake :(

Answer 7

It is fine man!