Question 137253: What is the solution to x^2-2x+5=0 when you use complex numbers. I always end up with 1-2i and 1+2i but when I put those into the equation to check it, it doesn't come out to be 0. Is that because it is a complex number and there truly is no solution? This question did not come from a textbook but from a worksheet from the tescher. The text we use is the Glencoe Algebra 2 text. It didn't help when I tried to follow the examples given.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the solution to x^2-2x+5=0 when you use complex numbers. I always end up with 1-2i and 1+2i but when I put those into the equation to check it, it doesn't come out to be 0.
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x^2-2x+5 = 0
x = [2 +- sqrt(4-4*5)]/2
x = [2 +- sqrt(-16)]/2
x = [2 +- 4i]/2
x = [1 +-2i]
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Checking x = 1+2i
(1+2i)^2 -2(1+2i) + 5 = 0
1-4+4i -2 -4i +5 = 0
(1-4-2+5)+(4i-4i) = 0
0 + 0i = 0
It checks
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Cheers,
Stan H.
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