Click right here to see ALL troubles on GraphsQuestion 421979: Please assist me leveling this equation: (4-2i)/(7+3i) discovered 2 remedies by shree840, Theo:Answer by shree840(260)
(Show Source): You have the right to put this systems on your website! (4-2i)(7+3i)remember i^2=-1use either foil technique or rest it upf very first 4*7=28o external 4*3i=12ii innner -2i*7=-14il last -2i*3i=-6i^2 =-6*-2=1228+12i-14i+12-2i+40 price by Theo(11661)
(Show Source): You can put this solution on her website! your expression is (4-2i) / (7 + 3i)I at first thought this was a multiplication, but I now see it"s a division.you would desire to remove the ns terms indigenous the denominator.if you main point both numerator and denominator through (7-3i), that must do it.your expression becomes:(4-2i) * (7-3i) separated by (7+3i) * (7-3i)(7+3i) * (7-3i) would be same to 49 - 21i + 21i - 9i^2the middle terms publication out and you room left with 49 -9i^2the i"s space treated like any kind of other variable until the end, at which time castle are finally processed based upon the rules for i handling to be defined after all is said and also done.anyway, her denominator is 49 - 9i^2you would multiply your numerator out to get:(4-2i) * (7-3i) = 28 - 12i - 14i + 6i^2combine like terms to acquire your numerator equal to 28 - 26i + 6i^2your expression now has actually become:28 - 26i + 6i^2 split by 49 - 9i^2now you process the i"s based upon the rules.i = ii^2 = -1i^3 = -ii^4 = 1this is a cyclical pattern that repeats every 4 exponents.i^5 = ii^6 = -1i^7 = -ii^8 = 1i^9 = ii^10 = -1i^11 = -ii^12 = 1etc.your expression is, when again:28 - 26i + 6i^2 separated by 49 - 9i^2since i^2 is equal to -1, you readjust your expression to become:28 - 26i + 6*(-1) separated by 49 - 9*(-1)this simplifies to:28 - 26i - 6 split by 49 + 9combine choose terms come get:22 - 26i split by 58divide both numerator and denominator by 2 come get:11 - 13i split by 29that must be your answer if ns did that right.here"s a decent reference that pretty much tells friend the very same thing.http://www.sparknotes.com/math/rememberingsomer.com2/complexnumbers/section3.rhtmlyou eliminate the facility number indigenous the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.if the denominator is a + bi, then the conjugate is a - biif the denominator is a - bi, then the conjugate is a + biboth the numerator and the denominator have to be multiplied by the same factor in stimulate to keep the truth of the expression.2/4 * 2/2 = 4/8the integrity of the expression is maintained due to the fact that 4/8 is indistinguishable to 2/4.between what i told you and the reference, girlfriend should gain the idea.