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Solve the Equation:

w 2 + 6 w + 34 = 0 w^{2} +6w +34=0

Giving your answer in the form p + q i p+qi , what is the value of p + ∣ q ∣ p +|q|


The answer is 2.

Callum Schafer by Callum Schafer , 22, United Kingdom

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2 solutions

Setting this into the quadratic formula: − 6 ± 6 2 − 4 ( 1 ) ( 36 ) 2 ( 1 ) = − 6 ± − 100 2 = − 6 ± 100 i 2 = − 3 ± 5 i \frac{-6\pm\sqrt{6^2-4(1)(36)}}{2(1)}=\frac{-6\pm\sqrt{-100}}{2}=\frac{-6\pm100i}{2}=-3\pm5i Setting p = − 3 p=-3 and q = 5 i q=5i , p + ∣ q ∣ = − 3 + 5 = 2 p+|q|=-3+5=\boxed{2}

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Callum Schafer
Jan 3, 2014

Using quadratic formula we get: ( w = ) − 6 + − 36 − 4 ( 34 ) 2 (w=) \frac{-6\frac{+}{-}\sqrt{36-4(34)}}{2}

Which simplifies to: − 6 + − − 100 2 \frac{-6\frac{+}{-}\sqrt{-100}}{2} − 6 + − 10 i 2 \frac{-6\frac{+}{-}10i}{2}

Giving us:

− 3 + − 5 i -3\frac{+}{-}5i

Substituting this into p + ∣ q ∣ p+|q|

Gives − 3 + 5 = 2 -3+5=2

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