Notes Over 5.4Imaginary Numbers

1i

9 19 i3

121 i11

22 1i

12 i

Notes Over 5.4Solving a Quadratic EquationSolving a Quadratic Equation

16 .1 2 x

x

Solve the equation.

x i4

52y 8

y 24

405 .2 2 y

16 5

y 8

y 22i

Notes Over 5.4Solving a Quadratic EquationSolving a Quadratic Equation

84 .3 2 r

r

Solve the equation.

r i2

22t 27

t 39

4682 .4 2 t

42

t 27

t 33i

4 42r 4

8 822t 54

Notes Over 5.4Solving a Quadratic EquationSolving a Quadratic Equation

025 .6 2 y

y

Solve the equation.

y i5

32x 12

x 34

3513 .5 2 x

253

x 12

t 32i

25 252y 25

1 123x 36

Notes Over 5.4Adding and Subtracting Complex NumbersAdding and Subtracting Complex Numbers

ii 2745 .7 12

Write the expression as a complex number in standard form.

ii 536 .8i6

1 i4 ii 65 .9

5 i7

Notes Over 5.4Adding and Subtracting Complex NumbersAdding and Subtracting Complex Numbers

ii 66 812 .10 6

Write the expression as a complex number in standard form.

ii 376 .11i2

3 i8 i108 21 .12 4 i10

Notes Over 5.4Multiplying Complex NumbersMultiplying Complex Numbers

ii 52 .13

i10

Write as a complex number in standard form.

ii 534 .14

22i

i12 220i ii 3232 .15 4 i6

i102

i1220

i6 29i 13

Notes Over 5.4Multiplying Complex NumbersMultiplying Complex Numbers

ii 624 .16 Write as a complex number in standard form.

235 .17 i

ii 28 .1816 i8 i2 2i1 15

8 i24 i2 26i 2 i26 ii 3535

25 i15 i15 29i 16 i30

i10

Notes Over 5.4Dividing Complex NumbersDividing Complex Numbers

i1

6 .19 6

Write as a complex number in standard form.

i6i1

i66

i1 1 i i 2i 1

2

3 3

1

i33

4

Notes Over 5.4Dividing Complex NumbersDividing Complex Numbers

i

i

2

5 .20 i10

Write as a complex number in standard form.

25ii2

i105

i2 i2 i2 2i 1

51 2

1

i21

5 2i

Notes Over 5.4Dividing Complex NumbersDividing Complex Numbers

i

i

5

32 .21

i2Write as a complex number in standard form.

23ii

i23

i

5

2i 1

Notes Over 5.4Dividing Complex NumbersDividing Complex Numbers

i

i

1

1 .22 1

Write as a complex number in standard form.

ii1

i2

i1 1

2

1i 2ii i

i

Notes Over 5.4