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: 57


$(3-\sqrt -5)(1+\sqrt -1)=(3+\sqrt 5)+(3-\sqrt 5)i$

Work Step by Step

$(3-\sqrt -5)(1+\sqrt -1)=3+3\sqrt -1-\sqrt -5-\sqrt -5\sqrt -1$. However we know that $i=\sqrt -1$ hence $3+3\sqrt -1-\sqrt -5-\sqrt -5\sqrt -1=3+3i-i\sqrt 5-i^{2}\sqrt 5$. We also know that $i^{2}=-1$ hence $3+3i-i\sqrt 5-i^{2}\sqrt 5=3+3i-i\sqrt 5+\sqrt 5$. By grouping the real and the imaginary parts we can write the solution in the form $a+bi$ where $a$ is the real and $b$ is the imaginary as $(3+\sqrt 5)+(3-\sqrt 5)i$
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