Answer Key 9.9

$3+8-4i$
$11-4i$
$3i-7i$
$-4i$
$7i-3+2i$
$9i-3$
$5-6-6i$
$-1-6i$
$-6i-3-7i$
$-13i-3$
$-8i-7i-5+3i$
$-12i-5$
$3-3i-7-8i$
$-4-11i$
$-4-i+1-5i$
$-3-6i$
$i-2-3i-6$
$-2i-8$
$5-4i+8-4i$
$13-8i$
$-48i^2$
$-48(-1)$
$48$
$-24i^2$
$-24(-1)$
$24$
$-40i^2$
$-40(-1)$
$40$
$-32i^2$
$-32(-1)$
$32$
$49i^2$
$49(-1)$
$-49$
$-7i^2(4-3i)$
$-28i^2+21i^3$
$-28(-1)+21(-1)i$
$28-21i$
$36+60i+25i^2$
$36+60i+25(-1)$
$36+60i-25$
$11+60i$
$16i^2(-2-8i)$
$32i^2+128i^3$
$32(-1)+128(-1)i$
$-32-128i$
$\begin{array}{rrrrrl} \\ \\ \\ \\ \\ &56&-&42i&& \\ &&+&32i&-&24i^2 \\ \midrule &56&-&10i&-&24(-1) \\ +&24&&&\Longleftarrow & \\ \midrule &80&-&10i&& \end{array}$
$9i^2(4-4i)$
$-36i^2+36i^3$
$-36(-1)+36(-1)i$
$36-36i$
$\begin{array}{rrrrrl} \\ \\ \\ \\ \\ &-8&+&10i&& \\ &&+&28i&-&35i^2 \\ \midrule &-8&+&38i&-&35(-1) \\ +&35&&&\Longleftarrow & \\ \midrule &27&+&38i&& \end{array}$
$-32i+64i+4+12i$
$-28+76i$
$\begin{array}{rrrrrl} \\ \\ \\ \\ \\ &32&+&24i&& \\ &&-&16i&-&12i^2 \\ \midrule &32&+&8i&-&12(-1) \\ +&12&&&\Longleftarrow & \\ \midrule &44&+&8i&& \end{array}$
$-18i+12i^2-28i^2$
$-18i+12(-1)-28(-1)$
$-18i-12+28$
$-18i+16$
$\begin{array}{rrrrrl} \\ \\ \\ \\ \\ &2&+&10i&& \\ &&+&i&+&5i^2 \\ \midrule &2&+&11i&+&5(-1) \\ -&5&&&\Longleftarrow & \\ \midrule &-3&+&11i&& \end{array}$
$\begin{array}{rrrrrl} \\ \\ \\ \\ \\ &-6&+&3i&& \\ &&+&10i&-&5i^2 \\ \midrule &-6&+&13i&-&5(-1) \\ +&5&&&\Longleftarrow & \\ \midrule &-1&+&13i&& \end{array}$
$\dfrac{-9+5i}{i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-9i+5i^2}{i^2}\Rightarrow \dfrac{-9i+5(-1)}{(-1)}\Rightarrow 9i+5$
$\dfrac{-3+2i}{-3i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-3i+2i^2}{-3i^2}\Rightarrow \dfrac{-3i+2(-1)}{-3(-1)}\Rightarrow \dfrac{-3i-2}{3}$
$\dfrac{-10i-9i}{6i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-10i-9i^2}{6i^2}\Rightarrow \dfrac{-10i-9(-1)}{6(-1)}\Rightarrow \dfrac{-10i+9}{-6}$
$\dfrac{-4+2i}{3i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-4i+2i^2}{3i^2}\Rightarrow \dfrac{-4i+2(-1)}{3(-1)}\Rightarrow \dfrac{-4i-2}{-3}$
$\dfrac{-3-6i}{4i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-3i-6i^2}{4i^2}\Rightarrow \dfrac{-3i-6(-1)}{4(-1)}\Rightarrow \dfrac{-3i+6}{4}$
$\dfrac{-5+9i}{9i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-5i+9i^2}{9i^2}\Rightarrow \dfrac{-5i+9(-1)}{9(-1)}\Rightarrow \dfrac{-5i-9}{-9}\Rightarrow \dfrac{5i+9}{9}$
$\dfrac{10-i}{-i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{10i-i^2}{-i^2}\Rightarrow \dfrac{10i-(-1)}{-(-1)}\Rightarrow 10i+1$
$\dfrac{10}{5i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{10i}{5i^2}\Rightarrow \dfrac{10i}{5(-1)}\Rightarrow \dfrac{10i\div -5}{-5\div -5}\Rightarrow -2i$
$\dfrac{4i}{-10+i}\cdot \dfrac{-10-i}{-10-i}\Rightarrow \dfrac{-40i-4i^2}{(-10)^2-(i)^2}\Rightarrow \dfrac{-40i-4(-1)}{100--1}\Rightarrow \dfrac{-40i+4}{101}$
$\dfrac{9i}{1-5i}\cdot \dfrac{1+5i}{1+5i}\Rightarrow \dfrac{9i+45i^2}{(1)^2-(5i)^2}\Rightarrow \dfrac{9i+45(-1)}{1-25i^2}\Rightarrow \dfrac{9i-45}{1-25(-1)}\Rightarrow \dfrac{9i-45}{1+25}\Rightarrow \\$
$\dfrac{9i-45}{26}$
$\dfrac{8}{7-6i}\cdot \dfrac{7+6i}{7+6i}\Rightarrow \dfrac{56+48i}{7^2-36i^2}\Rightarrow \dfrac{56+48i}{49-36(-1)}\Rightarrow \dfrac{56+48i}{49+36}\Rightarrow \dfrac{56+48i}{85}$
$\dfrac{4}{4+6i}\cdot \dfrac{4-6i}{4-6i}\Rightarrow \dfrac{16-24i}{16-36i^2}\Rightarrow \dfrac{16-24i}{16+36}\Rightarrow \dfrac{(16-24i)\div 4}{52\div 4} \Rightarrow \dfrac{4-6i}{13}$
$\dfrac{7}{10-7i}\cdot \dfrac{10+7i}{10+7i}\Rightarrow \dfrac{70+49i}{100-49i^2}\Rightarrow \dfrac{70+49i}{100+49}\Rightarrow \dfrac{70+49i}{149}$
$\dfrac{9}{-8-6i}\cdot \dfrac{-8+6i}{-8+6i}\Rightarrow \dfrac{-72+54i}{64-36i^2}\Rightarrow \dfrac{-72+54i}{64+36}\Rightarrow \dfrac{(-72+54i)\div 2}{100\div 2}\Rightarrow \\$
$\dfrac{-36+27i}{50}$
$\dfrac{5i}{-6-i}\cdot \dfrac{-6+i}{-6+i}\Rightarrow \dfrac{-30i+5i^2}{36-i^2}\Rightarrow \dfrac{-30i-5}{36+1}\Rightarrow \dfrac{-30i-5}{37}$
$\dfrac{8i}{6-7i}\cdot \dfrac{6+7i}{6+7i}\Rightarrow \dfrac{48i+56i^2}{36-49i^2}\Rightarrow \dfrac{48i-56}{36+49}\Rightarrow \dfrac{48i-56}{85}$
$\pm 9i$
$\sqrt{-5\cdot 9}\Rightarrow \pm 3\sqrt{5}i$
$\sqrt{-20}\Rightarrow \sqrt{-4\cdot 5}\Rightarrow \pm2\sqrt{5}i$
$\sqrt{24}\Rightarrow \sqrt{4\cdot 6}\Rightarrow \pm 2\sqrt{6}$
$\dfrac{3+\sqrt{3\cdot -9}}{6}\Rightarrow \dfrac{3+3\sqrt{3}i}{6}\Rightarrow \dfrac{1+\sqrt{3}i}{2}$
$\dfrac{-4-\sqrt{-2\cdot 4}}{-4}\Rightarrow \dfrac{-4-2\sqrt{2}i}{-4}\Rightarrow \dfrac{2+\sqrt{2}i}{2}$
$\dfrac{8-4i}{4}\Rightarrow 2-i$
$\dfrac{6+\sqrt{2\cdot -16}}{4}\Rightarrow \dfrac{6+4\sqrt{2}i}{4}\Rightarrow \dfrac{3+2\sqrt{2}i}{2}$
$i$
$i^3\Rightarrow -i$
1
1
$i^2\Rightarrow -1$
$i$
$i^2\Rightarrow -1$
$i^3\Rightarrow -i$

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