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Graphing Complex Numbers

Graphing Complex Numbers. Argand diagram. Imaginary. + -1 + 3i. + 3 + 2i. Real. Graphing Complex Numbers. Argand diagram. Imaginary. | z | = 2. 2. Circle radius = 2 centre (0,0). Real. Graphing Complex Numbers. Argand diagram. Imaginary. | z | < 2. 2.

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Graphing Complex Numbers

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  1. Graphing Complex Numbers Argand diagram Imaginary +-1 + 3i +3 + 2i Real

  2. Graphing Complex Numbers Argand diagram Imaginary | z | = 2 2 Circle radius = 2 centre (0,0) Real

  3. Graphing Complex Numbers Argand diagram Imaginary | z | < 2 2 Solid circle radius = 2 centre (0,0) but not including the circumference Real

  4. Graphing Complex Numbers Argand diagram Imaginary | z +1| = 2 1 Circle radius = 2 centre (-1,0) (-1,0) + Real

  5. Graphing Complex Numbers Argand diagram Imaginary | z +1-2i | = 3 (-1,2) + Circle radius = 3 centre (-1,2) r = 3 Real

  6. Graphing Complex Numbers Argand diagram Imaginary | z - 4 | = | z | There are 2 points (4,0) and (0,0) (0,0) + (4,0) + What you need is a line bisecting these points Real iex = 2

  7. Graphing Complex Numbers Argand diagram | z - 4 | = | z +1- 2i | Imaginary (-1,2) + There are 2 points (4,0) and (-1,2) (4,0) + What you need is a line bisecting these points Real ie 4y-10x +13 = 0

  8. Graphing Complex Numbers Argand diagram Imaginary z + z* = 8 a + bi + a - bi = 8 a = 4 2a = 8 a = 4 Real

  9. | z + 4 | = 3| z | Argand diagram | z + 4 |2 = 32| z |2 (z+4)(z*+4) = 9zz* Imaginary zz*+4z+4z*+16=9zz* 8zz*-4z-4z*=16 8zz*-4(z+z*)=16 If z = x+yi then z* =x-yi (½,0) + z+z*=2x and zz* = x2+y2 8x2 +8y2 - 8x = 16 Real x2 +y2 - x = 2 (x-½)2 +y2 = 2+½2 Circle centre (½,0) radius 3/2 (x-½)2 +y2 = 9/4 =(3/2)2

  10. | z + 4 | > 3| z | Argand diagram | z + 4 |2 > 32| z |2 (z+4)(z*+4*) > 9zz* Imaginary zz*+4z+4z*+16>9zz* 8zz*-4z-4z*<16 8zz*-4(z+z*)<16 If z = x+yi then z* =x-yi (½,0) + z+z*=2x and zz* = x2+y2 8x2 +8y2 - 8x < 16 Real x2 +y2 - x < 2 (x-½)2 +y2 < 2+½2 Circle centre (½,0) radius 3/2 (x-½)2 +y2 < 9/4 ie(3/2)2

  11. |z-4| < | z-2i | Argand diagram | z-4|2 < | z-2i |2 (z-4)(z*-4*) < (z-2i)(z*-2i*) -2i*=2i zz*-4z-4z*+16<zz*+2iz-2iz*+4 Imaginary 4z+4z*+2iz-2iz*>12 y<2x-3 4(z+z*)+2i(z-z*)>12 If z = x+yi then z* =x-yi z+z*=2x and z-z* = 2yi 8x +2i(2yi)> 12 Real 8x +4yi2 > 12 8x -4y > 12 2x - y > 3

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