Section 1
The Complex Numbers
Express the number in terms of $i$.$$\sqrt{-3}$$
Express the number in terms of $i$.$$\sqrt{-21}$$
Express the number in terms of $i$.$$\sqrt{-25}$$
Express the number in terms of $i$.$$\sqrt{-100}$$
Express the number in terms of $i$.$$-\sqrt{-33}$$
Express the number in terms of $i$.$$-\sqrt{-59}$$
Express the number in terms of $i$.$$-\sqrt{-81}$$
Express the number in terms of $i$.$$-\sqrt{-9}$$
Express the number in terms of $i$.$$\sqrt{-98}$$
Express the number in terms of $i$.$$\sqrt{-28}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-5+3 i)+(7+8 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-6-5 i)+(9+2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(4-9 i)+(1-3 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(7-2 i)+(4-5 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(12+3 i)+(-8+5 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-11+4 i)+(6+8 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-1-i)+(-3-i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-5-i)+(6+2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(3+\sqrt{-16})+(2+\sqrt{-25})$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(7-\sqrt{-36})+(2+\sqrt{-9})$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(10+7 i)-(5+3 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-3-4 i)-(8-i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(13+9 i)-(8+2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-7+12 i)-(3-6 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(6-4 i)-(-5+i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(8-3 i)-(9-i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-5+2 i)-(-4-3 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-6+7 i)-(-5-2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(4-9 i)-(2+3 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(10-4 i)-(8+2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\sqrt{-4} \cdot \sqrt{-36}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\sqrt{-49} \cdot \sqrt{-9}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\sqrt{-81} \cdot \sqrt{-25}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\sqrt{-16} \cdot \sqrt{-100}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$7 i(2-5 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$3 i(6+4 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$-2 i(-8+3 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$-6 i(-5+i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(1+3 i)(1-4 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(1-2 i)(1+3 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(2+3 i)(2+5 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(3-5 i)(8-2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-4+i)(3-2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(5-2 i)(-1+i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(8-3 i)(-2-5 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(7-4 i)(-3-3 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(3+\sqrt{-16})(2+\sqrt{-25})$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(7-\sqrt{-16})(2+\sqrt{-9})$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(5-4 i)(5+4 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(5+9 i)(5-9 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(3+2 i)(3-2 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(8+i)(8-i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(7-5 i)(7+5 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(6-8 i)(6+8 i)$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(4+2 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(5-4 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-2+7 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-3+2 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(1-3 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(2-5 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-1-i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(-4-2 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(3+4 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$(6+5 i)^{2}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{3}{5-11 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{i}{2+i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{5}{2+3 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{-3}{4-5 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{4+i}{-3-2 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{5-i}{-7+2 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{5-3 i}{4+3 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{6+5 i}{3-4 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{2+\sqrt{3} i}{5-4 i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{\sqrt{5}+3 i}{1-i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{1+i}{(1-i)^{2}}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{1-i}{(1+i)^{2}}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{4-2 i}{1+i}+\frac{2-5 i}{1+i}$$
Simplify. Write answers in the form $a+b i$, where a and $b$ are real numbers.$$\frac{3+2 i}{1-i}+\frac{6+2 i}{1-i}$$
Simplify.$$i^{11}$$
Simplify.$$i^{7}$$
Simplify.$$i^{35}$$
Simplify.$$i^{24}$$
Simplify.$$i^{64}$$
Simplify.$$i^{42}$$
Simplify.$$(-i)^{71}$$
Simplify.$$(-i)^{6}$$
Simplify.$$(5 i)^{4}$$
Simplify.$$(2 i)^{5}$$
Write a slope-intercept equation for the line containing the point (3,-5) and perpendicular to the line $3 x-6 y=7$.
Given that $f(x)=x^{2}+4$ and $g(x)=3 x+5$, find each of the following.The domain of $f-g$
Given that $f(x)=x^{2}+4$ and $g(x)=3 x+5$, find each of the following.The domain of $f / g$.
Given that $f(x)=x^{2}+4$ and $g(x)=3 x+5$, find each of the following.$$(f-g)(x)$$
Given that $f(x)=x^{2}+4$ and $g(x)=3 x+5$, find each of the following.$$(f / g)(2)$$
For the function $f(x)=x^{2}-3 x+4$ construct and simplify the difference quotient$$\frac{f(x+h)-f(x)}{h}$$
Determine whether the statement is true or false.The sum of two numbers that are complex conjugates of each other is always a real number.
Determine whether the statement is true or false.The conjugate of a sum is the sum of the conjugates of the individual complex numbers.
Determine whether the statement is true or false.The conjugate of a product is the product of the conjugates of the individual complex numbers.
Let $z=a+b i$ and $\bar{z}=a-b i$.Find a general expression for $1 / z$.
Let $z=a+b i$ and $\bar{z}=a-b i$.Find a general expression for $z \bar{z}$
Let $z=a+b i$ and $\bar{z}=a-b i$.Solve $z+6 \bar{z}=7$ for $z$
Let $z=a+b i$ and $\bar{z}=a-b i$.Multiply and simplify:$$[x-(3+4 i)][x-(3-4 i)]$$.