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Manipulate real and complex numbers and solve equations. AS 91577. Worksheet 1. Quadratics. General formula:. General solution:. Example 1. Equation cannot be factorised. Using quadratic formula. We use the substitution. A complex number. The equation has 2 complex solutions. Imaginary.

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Manipulate real and complex numbers and solve equations


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    1. Manipulate real and complex numbers and solve equations AS 91577

    2. Worksheet 1

    3. Quadratics General formula: General solution:

    4. Example 1 Equation cannot be factorised.

    5. Using quadratic formula We use the substitution A complex number

    6. The equation has 2 complex solutions Imaginary Real

    7. Equation has 2 complex solutions.

    8. Example 2

    9. Example 2

    10. Example 2

    11. Adding complex numbers Subtracting complex numbers

    12. Example

    13. Example

    14. (x + yi)(u + vi) = (xu – yv) + (xv + yu)i. Multiplying Complex Numbers

    15. Example

    16. Example

    17. Example 2

    18. Conjugate If The conjugate of z is If The conjugate of z is

    19. Dividing Complex Numbers

    20. Example

    21. Example

    22. Example

    23. Solving by matching terms Match real and imaginary Real Imaginary

    24. Solving polynomials Quadratics: 2 solutions 2 real roots 2 complex roots

    25. If coefficients are all real, imaginary roots are in conjugate pairs

    26. If coefficients are all real, imaginary roots are in conjugate pairs

    27. Cubic Cubics: 3 solutions 3 real roots 1 real and 2 complex roots

    28. Quartic Quartic: 4 solutions 2 real and 2 imaginary roots 4 real roots 4 imaginary roots

    29. Solving a cubic This cubic must have at least 1 real solutions Form the quadratic. Solve the quadratic for the other solutions x = 1, -1 - i, 1 + i

    30. Finding other solutions when you are given one solution. Because coefficients are real, roots come in conjugate pairs so Form the quadratic i.e. Form the cubic:

    31. Argand Diagram

    32. Just mark the spot with a cross

    33. Plot z = 3 + i z

    34. z = i z = -1 z =1 z = -i

    35. Multiplying a complex number by a real number.(x + yi) u = xu + yu i.

    36. Multiplying a complex number by i.zi = (x + yi) i = –y + xi.

    37. Reciprocal of z Conjugate

    38. Rectangular to polar form Using Pythagoras Modulus is the length Argument is the angle Check the quadrant of the complex number

    39. Modulus is the length

    40. Example 1 Rectangular form Polar form

    41. Example 2

    42. Example 3

    43. Converting from polar to rectangular

    44. Multiplying numbers in polar form Example 1

    45. Multiplying numbers in polar form Example 2 Take out multiples of