# Complex Number -- Solve for T and U

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Okay I have hit another stumbling block, I myself and trying hard to solve it alone but figured this is a doozy and I'll need some assistance. Correspondance has only 1 downfall - no teachers. Given: x^2 - 6x + 73 = 0 x = T +- U I must solve for T and U. Answer Key: T = 3 U = 8i Nothing like this was covered in the examples, so I am beside myself.

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Just in case you don't know off by heart:
For a quadratic of form: ax2 + bx + c

x = (-b +- Sqrt(b2 - 4*a*c))/(2*a)

Using this formula for your problem we get: a = 1, b = -6 and c = 73

Therefore:

x = (6 +- Sqrt(36 - 4*1*73)) / 2

x = (6 +- Sqrt(-256)) / 2

x = 3 +- Sqrt(-64)

Therefore T = 3 and U = 8i

Solved.

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Alternatively, you can use the properties of the sum and the product of the solutions to find the answer:

(T + U) + (T - U) = -b/a (always true for the sum of the two solutions to a quadratic equation)
2T = -(-6/1)
2T = 6
T = 3

(T + U) * (T - U) = c (always true for the product of the two solutions to a quadratic equation)
T2 - U2 = c
9 - U2 = 73
-U2 = 64
U2 = -64
U = 8i

Those two properties can be verified directly from the quadratic formula (in case you were wondering).

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