Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 70

Answer

$t=-\dfrac{3}{2}\pm\dfrac{\sqrt{3}}{2}i$

Work Step by Step

$t+3+\dfrac{3}{t}=0$ Multiply the whole equation by $t$: $t\Big(t+3+\dfrac{3}{t}=0\Big)$ $t^{2}+3t+3=0$ Use the quadratic formula to solve this equation. The formula is $t=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=3$ and $c=3$. Substitute the known values in the formula: $t=\dfrac{-3\pm\sqrt{3^{2}-4(1)(3)}}{2(1)}=\dfrac{-3\pm\sqrt{9-12}}{2}=...$ $...=\dfrac{-3\pm\sqrt{-3}}{2}=\dfrac{-3\pm\sqrt{3}i}{2}=-\dfrac{3}{2}\pm\dfrac{\sqrt{3}}{2}i$ The answer is $t=-\dfrac{3}{2}\pm\dfrac{\sqrt{3}}{2}i$
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