## Section6.4Additional Practice Related to Imaginary and Complex Numbers

### ExercisesExercises

###### 1.

$\sqrt{-81}$

Solution

$\sqrt{-81}=9i$

###### 2.

$-\sqrt{-144}$

Solution

$-\sqrt{-144}=-12i$

###### 3.

$\sqrt{-\frac{9}{25}}$

Solution

$\sqrt{-\frac{9}{25}}=\frac{3}{5}i$

###### 4.

$-\sqrt{-90}$

Solution

$-\sqrt{-90}=-3\sqrt{10}i$

###### 5.

$\sqrt{-325}$

Solution

$\sqrt{-325}=5\sqrt{13}i$

###### 6.

$\sqrt{-\frac{27}{64}}$

Solution

$\sqrt{-\frac{27}{64}}=\frac{3\sqrt{3}}{8}i$

Simplify each of the following expressions. Please note that your final expression should be of the form $a\text{,}$ $bi\text{,}$ or $a+bi$ where $a$ and/or $b$ are real number(s).

###### 7.

$(7i)(4i)$

Solution

$(7i)(4i)=-28$

###### 8.

$(-2i)\left(\frac{3}{4}i\right)$

Solution

$(-2i)\left(\frac{3}{4}i\right)=\frac{3}{2}$

###### 9.

$(-i)(-7i)$

Solution

$(-i)(-7i)=-7$

###### 10.

$\frac{3}{i}$

Solution

$\frac{3}{i}=-3i$

###### 11.

$-\frac{5}{11i}$

Solution

$-\frac{5}{11i}=\frac{5}{11}i$

###### 12.

$(3i)(12i)\left(\frac{5}{6}i\right)$

Solution

$(3i)(12i)\left(\frac{5}{6}i\right)=-30i$

###### 13.

$i^{107}$

Solution

$i^{107}=-i$

###### 14.

$i^{7981}$

Solution

$i^{7981}=i$

###### 15.

$i^{-15}$

Solution

$i^{-15}=i$

###### 16.

$i^{-14}$

Solution

$i^{-14}=-1$

###### 17.

$(5-4i)(-3+2i)$

Solution

$(5-4i)(-3+2i)=-7+22i$

###### 18.

$(2-i)^2$

Solution

$(2-i)^2=3-4i$

###### 19.

$(8-3i)(8+3i)$

Solution

$(8-3i)(8+3i)=73$

###### 20.

$\frac{24}{1-3i}$

Solution

$\frac{24}{1-3i}=\frac{12}{5}+\frac{36}{5}i$

###### 21.

$-\frac{169i}{5+12i}$

Solution

$-\frac{169i}{5+12i}=-12-5i$

###### 22.

$-\frac{1-2i}{1+2i}$

Solution

$-\frac{1-2i}{1+2i}=\frac{3}{5}+\frac{4}{5}i$

###### 23.

$\frac{2+5i}{2-5i}$

Solution

$\frac{2+5i}{2-5i}=-\frac{21}{29}+\frac{20}{29}i$

###### 24.

$\frac{-2-3i}{-2+3i}$

Solution

$\frac{-2-3i}{-2+3i}=-\frac{5}{13}+\frac{12}{13}i$