X2 t01 05 conjugate properties (2013)

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X2 t01 05 conjugate properties (2013)

  1. 1. Properties of Complex Conjugates
  2. 2. Properties of Complex Conjugates 1 z  z
  3. 3. Properties of Complex Conjugates 1 z  z 2 arg z   arg z
  4. 4. Properties of Complex Conjugates 1 z  z 2 arg z   arg z 3 zz  x 2  y 2 z 2
  5. 5. Properties of Complex Conjugates 1 z  z 2 arg z   arg z 3 zz  x 2  y 2 z 2 4 z1  z2  z1  z2
  6. 6. Properties of Complex Conjugates 1 z  z 5 z1 z2  z1  z2 2 arg z   arg z 3 zz  x 2  y 2 z 2 4 z1  z2  z1  z2
  7. 7. Properties of Complex Conjugates 1 z  z 5 z1 z2  z1  z2 2 arg z   arg z 3 zz  x 2  y 2 z 2 4 z1  z2  z1  z2  z1  z1 6     z2  z2
  8. 8. Properties of Complex Conjugates 1 z  z 5 z1 z2  z1  z2 2 arg z   arg z 3 zz  x 2  y 2 z  z1  z1 6     z2  z2 2 4 z1  z2  z1  z2 1 z 7   2 z z
  9. 9. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i
  10. 10. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i
  11. 11. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i
  12. 12. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i  6  2i   x  iy      3i  2
  13. 13. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i  6  2i   x  iy      3i  6  2i  3i 2
  14. 14. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i  6  2i   x  iy      3i  6  2i  3i 6  2i 2  x  iy   2 3i 2
  15. 15. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i Multiply 1  2  6  2i   x  iy      3i  6  2i  3i 6  2i 2  x  iy   2 3i 2
  16. 16. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i Multiply 1  2 6  2i 6  2i  x  iy   x  iy    3i 3i 2 2  6  2i   x  iy      3i  6  2i  3i 6  2i 2  x  iy   2 3i 2
  17. 17. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i Multiply 1  2 6  2i 6  2i  x  iy   x  iy    3i 3i 36  4 2 2 2 x  y   9 1 4 2 2  6  2i   x  iy      3i  6  2i  3i 6  2i 2  x  iy   2 3i 2
  18. 18. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i Multiply 1  2 6  2i 6  2i  x  iy   x  iy    3i 3i 36  4 2 2 2 x  y   9 1 4 x2  y2  2 2 2  6  2i   x  iy      3i  6  2i  3i 6  2i 2  x  iy   2 3i 2
  19. 19. 6  2i e.g. If x  iy  , show that x 2  y 2  2 3i 6  2i x  iy  3i 6  2i 2  x  iy   1 3i Multiply 1  2 6  2i 6  2i  x  iy   x  iy    3i 3i 36  4 2 2 2 x  y   9 1 4 x2  y2  2 2  6  2i   x  iy      3i  6  2i  3i 6  2i 2  x  iy   2 3i 2 2 Exercise 4H; 1 to 6

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