Lesson 8 Complex Computations Practice Understanding

Ready

Solve each system of equations.

1.

${\begin{cases} y = 3 x \\ y = - 2 x - 15 \end{cases}$

2.

${\begin{cases} 3 x + y = 21 \\ y = - 2 x - 15 \end{cases}$

3.

${\begin{cases} 3 x + 2 y = 7 \\ x - 2 y = - 3 \end{cases}$

4.

${\begin{cases} 5 x - y = 13 \\ - 2 x + y = - 1 \end{cases}$

5.

${\begin{cases} 3 x + y = 21 \\ - 3 x + 5 y = - 3 \end{cases}$

6.

${\begin{cases} 3 x + 2 y = 7 \\ x + y = 2 \end{cases}$

Set

Perform the indicated operation.

7.

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

8.

$(6 - 4 i) - (7 + 2 i)$

9.

$3 (5 + 2 i)$

10.

$(9 - 2 i) (1 + 3 i)$

11.

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

12.

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

Name the conjugate for each complex number.

13.

$5 + 2 i$

14.

$7 - 12 i$

15.

$21 - 9 i$

16.

$13 + 4 i$

Divide the complex numbers.

17.

$\frac{3 - 5 i}{2 + 5 i}$

18.

$\frac{6 + 7 i}{4 - 3 i}$

19.

$\frac{2 - 3 i}{1 - 6 i}$

Find the modulus for each complex number.

20.

$3 - 5 i$

21.

$4 - 3 i$

22.

$- 4 + 3 i$

23.

If the graphical representation of the operations between two complex numbers results in a value along the $y$ -axis or imaginary axis, what must be true about the two complex numbers?

24.

If the graphical representation of the operations between two complex numbers results in a value along the $x$ -axis or real number axis, what must be true about the two complex numbers?

Go

25.

List the strategies that can be used to solve quadratic equations. Explain when each of the strategies would be most efficient. Give an example of a quadratic equation that would be most efficiently solved for each.

Solve.

26.

$x^{2} + 9 x + 18 = 0$

27.

$x^{2} - 2 x - 3 = 0$

28.

$2 x^{2} - 5 x + 3 = 0$

29.

$(x - 2) (x + 3) = 0$

30.

$10 x^{2} - x + 9 = 0$

31.

${(x - 2)}^{2} = 20$

32.

$2 x^{2} - 2 x + 13 = 0$

33.

$4 x^{2} - 2 x + 1 = 0$

34.

$x^{2} + x + 9 = 0$