Recognize Patterns
Solve each equation over the Complex number system. As you work through the problems, look for and make use of structure. Does a previous question help you solve the next problem?
1) \(0=(x-2)\)
2) \(0=(x-3)\)
3) \(0=(x-2)(x-3)\)
4) \(0=(x-2)(x+2)\)
5) \(0=x(x-2)\)
6) \(0=x^2-3x\)
7) \(0=x^2-9\)
8) \(0=x^2-3x-10\)
9) \(0=x^3-3x^2-10x\)
10) \(0=x^2+16\)
11) \(0=x^2+x+5\)
12) \(0=(x^2-9)(x^2-3x-10)\)
13) \(0=(x^2-3x-4)(x-1)\)
14) \(0=(x^2+16)(x^2-16)\)
15) \(0=(x^2+25)(x^2+x+5)\)
16) \(0=x^3-8\)
17) \(0=27x^3+8\)
18) \(0=27x^4+8x\)
Solutions
Solve each equation over the Complex number system. As you work through the problems, look for and make use of structure. Does a previous question help you solve the next problem?
1) \(0=(x-2)\)
2) \(0=(x-3)\)
3) \(0=(x-2)(x-3)\)
4) \(0=(x-2)(x+2)\)
5) \(0=x(x-2)\)
6) \(0=x^2-3x\)
7) \(0=x^2-9\)
8) \(0=x^2-3x-10\)
9) \(0=x^3-3x^2-10x\)
10) \(0=x^2+16\)
11) \(0=x^2+x+5\)
12) \(0=(x^2-9)(x^2-3x-10)\)
13) \(0=(x^2-3x-4)(x-1)\)
14) \(0=(x^2+16)(x^2-16)\)
15) \(0=(x^2+25)(x^2+x+5)\)
16) \(0=x^3-8\)
17) \(0=27x^3+8\)
18) \(0=27x^4+8x\)
Solutions