4.3E: Exercises
- Page ID
- 104855
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Practice Makes Perfect
In the following exercises, write each expression in terms of \(i\) and simplify if possible.
- a. \(\sqrt{-16}\) b. \(\sqrt{-11}\) c. \(\sqrt{-8}\)
- a. \(\sqrt{-100}\) b. \(\sqrt{-13}\) c. \(\sqrt{-45}\)
- Answer
-
1. a. \(4i\) b. \(i\sqrt{11}\) c. \(2i\sqrt{2}\)
2. a. \(10i\) b. \(i\sqrt{13}\) c. \(3i\sqrt{5}\)
In the following exercises, add or subtract, putting the answer in \(a + bi\) form.
- \(\sqrt{-75}+\sqrt{-48}\)
- \(\sqrt{-50}+\sqrt{-18}\)
- \((1+3 i)+(7+4 i)\)
- \((8-i)+(6+3 i)\)
- \((1-4 i)-(3-6 i)\)
- \((6+i)-(-2-4 i)\)
- \((5-\sqrt{-36})+(2-\sqrt{-49})\)
- \((-7-\sqrt{-50})-(-32-\sqrt{-18})\)
- Answer
-
- \(0+\left(9\sqrt{3}\right)i\)
- \(0+\left(8\sqrt{2}\right)i\)
- \(8+7i\)
- \(14+2i\)
- \(-2+2i\)
- \(8+5i\)
- \(7-13i\)
- \(25-\left(2 \sqrt{2}\right) i\)
In the following exercises, multiply, putting the answer in \(a+bi\) form.
- \(4 i(5-3 i)\)
- \(-6 i(-3-2 i)\)
- \((4+3 i)(-5+6 i)\)
- \((-3+3 i)(-2-7 i)\)
- Answer
-
- \(12+20i\)
- \(-12+18i\)
- \(-38+9 i\)
- \(27+15i\)
In the following exercises, multiply using the Product of Binomial Squares Pattern, putting the answer in \(a+bi\) form.
- \((3+4 i)^{2}\)
- \((-1+5 i)^{2}\)
- \((-2-3 i)^{2}\)
- \((-6-5 i)^{2}\)
- Answer
-
- \(-7+24i\)
- \(-24-10i\)
- \(-5-12i\)
- \(11+60i\)
In the following exercises, multiply using the Product of Complex Conjugates Pattern.
- \((7-i)(7+i)\)
- \((6-5 i)(6+5 i)\)
- \((9-2 i)(9+2 i)\)
- \((-3-4 i)(-3+4 i)\)
- Answer
-
- \(50\)
- \(61\)
- \(85\)
- \(25\)
In the following exercises, divide, putting the answer in \(a+bi\) form.
- \(\dfrac{3+4 i}{4-3 i}\)
- \(\dfrac{2+i}{3-4 i}\)
- \(\dfrac{3}{2-3 i}\)
- \(\dfrac{-4}{3-2 i}\)
- \(\dfrac{1+4 i}{3 i}\)
- \(\dfrac{-2-3 i}{4 i}\)
- Answer
-
- \(0 + i\)
- \(\frac{2}{25}+\frac{11}{25} i\)
- \(\frac{6}{13}+\frac{9}{13} i\)
- \(-\frac{12}{13}-\frac{8}{13} i\)
- \(\frac{4}{3}-\frac{1}{3} i\)
- \(-\frac{3}{4}+\frac{1}{2} i\)