document.write( "Question 543659: I need help with finding the complex number z that satisfies this equation: z*(2-i)=3+i Thank you :) \n" ); document.write( "

Algebra.Com's Answer #354922 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
z*(2-i) = 3 + i
\n" ); document.write( "Divide both sides by (2-i)
\n" ); document.write( "z = $\"%28%283%2Bi%29%29%2F%28%282-i%29%29\"$
\n" ); document.write( "multiply by the conjugate of the denominator over itself, (same as mult by 1)
\n" ); document.write( "z = $\"%28%283%2Bi%29%29%2F%28%282-i%29%29\"$ * $\"%28%282%2Bi%29%29%2F%28%282%2Bi%29%29\"$
\n" ); document.write( "FOIL
\n" ); document.write( "z = $\"%28%286%2B3i%2B2i%2Bi%5E2%29%29%2F%28%284-i%5E2%29%29\"$
\n" ); document.write( "we know i^2 = -1
\n" ); document.write( "z = $\"%28%286%2B5i-1%29%29%2F%28%284-%28-1%29%29%29\"$ = $\"%28%285%2B5i%29%29%2F%28%284%2B1%29%29%29\"$
\n" ); document.write( "which is
\n" ); document.write( "z = $\"%28%285%2B5i%29%29%2F%285%29%29\"$
\n" ); document.write( "cancel the 5
\n" ); document.write( "z = 1 + i
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this; replace (1+i) for z in the original equation
\n" ); document.write( "(1+i)*(2-i) = 3 + i
\n" ); document.write( "FOIL
\n" ); document.write( "2-i+2i-i^2 = 3 + i
\n" ); document.write( "2 + i -(-1) = 3 + i
\n" ); document.write( "3 + i + 2 = 3 + i
\n" ); document.write( "3 + i = 3 + i; success! \n" ); document.write( "

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