Question

The complex solution to a quadratic equation is below. Write this solution in standard form, a+bi, where a and b are real numbers. What are the values of a and b.

Answer 1

Answers:    a = 1/4,    b = 2

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Work Shown:

sqrt(-256) = sqrt(-1*256)

sqrt(-256) = sqrt(-1)*sqrt(256)

sqrt(-256) = i*16

sqrt(-256) = 16i

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The given equation

$x = \frac{2\pm\sqrt{-256}}{8}$

turns into

$x = \frac{2\pm16i}{8}$

$x = \frac{2}{8}\pm \frac{16}{8}i$

$x = \frac{1}{4}\pm 2i$

Compare this to $x = a \pm bi$ and we see that a = 1/4 and b = 2.