x2 t01 05 conjugate properties (2013)

Properties of Complex

Conjugates

Properties of Complex

Conjugates zz 1

Properties of Complex

Conjugates zz 1

zz argarg 2

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

2121 4 zzzz

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

2121 4 zzzz

2121 5 zzzz

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

2121 4 zzzz

2121 5 zzzz

2

1

2

1 6z

z

z

z

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

2121 4 zzzz

2121 5 zzzz

2

1

2

1 6z

z

z

z

2

1 7

z

z

z

2 that show ,3

26 If 22

yx

i

iiyxe.g.

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

13

26

2 i

iiyx

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

13

26

2 i

iiyx

i

iiyx

3

26

2

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

13

26

2 i

iiyx

i

iiyx

3

26

2

i

i

3

26

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

13

26

2 i

iiyx

i

iiyx

3

26

2

i

i

3

26

23

26

2 i

iiyx

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

21Multiply

13

26

2 i

iiyx

i

iiyx

3

26

2

i

i

3

26

23

26

2 i

iiyx

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

21Multiply

i

i

i

iiyxiyx

3

26

3

26

22

13

26

2 i

iiyx

i

iiyx

3

26

2

i

i

3

26

23

26

2 i

iiyx

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

21Multiply

i

i

i

iiyxiyx

3

26

3

26

22

13

26

2 i

iiyx

i

iiyx

3

26

2

i

i

3

26

23

26

2 i

iiyx

4

19

436

222

yx

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

21Multiply

i

i

i

iiyxiyx

3

26

3

26

22

13

26

2 i

iiyx

i

iiyx

3

26

2

i

i

3

26

23

26

2 i

iiyx

4

19

436

222

yx

2 22 yx

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

21Multiply

i

i

i

iiyxiyx

3

26

3

26

22

13

26

2 i

iiyx

i

iiyx

3

26

2

i

i

3

26

23

26

2 i

iiyx

4

19

436

222

yx

2 22 yx

Exercise 4H; 1 to 6