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Warm-up:

Warm-up:. Math ador Gameplan. Section 9.6: Polar Form of Complex Numbers CA Standards: T15.0 Daily Objective (3/13/13): Students will be able to graph complex numbers in complex plane and convert complex numbers between polar and rectangular forms. Homework: page 590 (#16 to 44 all).

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Warm-up:

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  1. Warm-up:

  2. MathadorGameplan Section 9.6:Polar Form of Complex Numbers CA Standards: T15.0 Daily Objective (3/13/13): Students will be able to graph complex numbers in complex plane and convert complex numbers between polar and rectangular forms. Homework:page 590 (#16 to 44 all)

  3. Absolute value of a Complex Number

  4. Solve the equation 2x + y + 3i = 9 + xi – yi for x and y, where x and y are real numbers 2x + y + 3i = 9 + xi – yi (2x + y) + 3i = 9 + (x – y)i So, 2x + y = 9 and x – y = 3 x = 4 and y = 1 Solving complex equations

  5. Solve the equation 2x + y + xi + yi = 5 + 4i for x and y, where x and y are real numbers x = 1 and y = 3 Practice

  6. Now, any Complex Number can be expressed as: x + yi That number can be plotted as on ordered pair (x, y) Complex Plane Imaginary Axis Real Axis

  7. Absolute value of a Complex Number

  8. a. z = 3 + 2i b. z = 4i Graph and find the absolute value

  9. Remember these relationships between polar and rectangular form: Expressing Complex Numbers in Polar Form So any complex number, x + yi, can be written in polar form:

  10. Polar form of a complex number Here is the shorthand way of writing polar form: r is called the modulus θ is called the argument

  11. Rewrite the following complex number in polar form: 4 – 4i Expressing Complex Numbers in Polar Form

  12. Expressing Complex Numbers in Polar Form Express the following complex number in polar form: 5i

  13. practice

  14. Converting to Rectangular form Express the following complex number in rectangular form:

  15. Converting to rectangular form Rewrite the following complex number in rectangular form:

  16. Write z = 2(cos π/3+ i sin π/3) in rectangular form. Write z = 4 cis π/6in rectangular form. practice

  17. ICE #1 Solve the equation 3x + 2y – 7i = 12 + xi – 3yi x = 2 y = 3

  18. ICE #2 Graph each number in the complex plane and find its absolute value z = 4 + 3i z = 2.5i |z| = 5 |z| = 2.5

  19. ICE #3 Plot the first four members of the orbit of zo= 0.9 + 0.7i under iteration by f(z) = z2

  20. ICE #4 Express each complex number in polar form 1 – 4i -3 – 2i

  21. ICE #5 Graph Then express it in rectangular form

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