College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.5 - Complex Numbers - 1.5 Exercises - Page 131: 70


$\displaystyle -\frac{3}{2}\pm\frac{\sqrt{3}}{2}i$

Work Step by Step

First we multiply through by $t$: $t+3+\displaystyle \frac{3}{t}=0$ $t^{2}+3t+3=0$ Next we use the quadratic formula ($a=1, b=3, c=3$): $\displaystyle t=\frac{-3\pm\sqrt{(3)^{2}-4*1*3}}{2(1)}=\frac{-3\pm\sqrt{9-12}}{2}=\frac{-3\pm\sqrt{-3}}{2}=\frac{-3\pm \sqrt{3}i}{2}=-\frac{3}{2}\pm\frac{\sqrt{3}}{2}i$
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