x2 t01 06 conjugate properties (2011)

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Page 1: X2 T01 06 conjugate properties (2011)

Properties of Complex

Conjugates

Page 2: X2 T01 06 conjugate properties (2011)

Properties of Complex

Conjugates zz 1

Page 3: X2 T01 06 conjugate properties (2011)

Properties of Complex

Conjugates zz 1

zz argarg 2

Page 4: X2 T01 06 conjugate properties (2011)

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

Page 5: X2 T01 06 conjugate properties (2011)

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

2121 4 zzzz

Page 6: X2 T01 06 conjugate properties (2011)

Properties of Complex

Conjugates zz 1

zz argarg 2

2

22 3

z

yxzz

2121 4 zzzz

2121 5 zzzz

Page 7: X2 T01 06 conjugate properties (2011)

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

Page 8: X2 T01 06 conjugate properties (2011)

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

Page 9: X2 T01 06 conjugate properties (2011)

2 that show ,3

26 If 22

yx

i

iiyxe.g.

Page 10: X2 T01 06 conjugate properties (2011)

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

Page 11: X2 T01 06 conjugate properties (2011)

2 that show ,3

26 If 22

yx

i

iiyxe.g.

i

iiyx

3

26

13

26

2 i

iiyx

Page 12: X2 T01 06 conjugate properties (2011)

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

Page 13: X2 T01 06 conjugate properties (2011)

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

Page 14: X2 T01 06 conjugate properties (2011)

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

Page 15: X2 T01 06 conjugate properties (2011)

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

Page 16: X2 T01 06 conjugate properties (2011)

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

Page 17: X2 T01 06 conjugate properties (2011)

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

Page 18: X2 T01 06 conjugate properties (2011)

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

Page 19: X2 T01 06 conjugate properties (2011)

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