graphing complex numbers
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Graphing Complex Numbers
Real
Imaginary
+ 3 + 2i
+ -1 + 3i
Argand diagram
Graphing Complex Numbers
Real
Imaginary
Argand diagram
| z | = 22
Circle radius = 2 centre (0,0)
Graphing Complex Numbers
Real
Imaginary
Argand diagram
| z | < 2
2Solid circle radius = 2 centre (0,0) but not including the circumference
Graphing Complex Numbers
Real
Imaginary
Argand diagram
| z +1| = 21
Circle radius = 2 centre (-1,0)(-1,0)
+
Graphing Complex Numbers
Real
Imaginary
Argand diagram
| z +1-2i | = 3
r = 3
Circle radius = 3 centre (-1,2)
(-1,2) +
Graphing Complex Numbers
Real
Imaginary
Argand diagram
| z - 4 | = | z |
ie x = 2
There are 2 points (4,0) and (0,0)(4,0)
+(0,0) +
What you need is a line bisecting these points
Graphing Complex Numbers
Real
Imaginary
Argand diagram
| z - 4 | = | z +1- 2i |
ie 4y -10x +13 = 0
There are 2 points (4,0) and (-1,2)
(4,0) +
(-1,2) +
What you need is a line bisecting these points
Graphing Complex Numbers
Real
Imaginary z + z* = 8
Argand diagram
a + bi + a - bi = 8
2a = 8
a = 4
a = 4
Real
Imaginary
Argand diagram| z + 4 | = 3| z |
z+z*=2x and zz* = x2+y2
zz*+4z+4z*+16=9zz*
(½,0) +
If z = x+yi then z* =x-yi
| z + 4 |2 = 32| z |2
(z+4)(z*+4) = 9zz*
8zz*-4z-4z*=16
8zz*-4(z+z*)=16
8x2 +8y2 - 8x = 16
x2 +y2 - x = 2(x-½)2 +y2 = 2+½2
(x-½)2 +y2 = 9/4 =(3/2)2Circle centre (½,0) radius 3/2
Real
Imaginary
Argand diagram| z + 4 | > 3| z |
z+z*=2x and zz* = x2+y2
zz*+4z+4z*+16>9zz*
(½,0) +
If z = x+yi then z* =x-yi
| z + 4 |2 > 32| z |2
(z+4)(z*+4*) > 9zz*
8zz*-4z-4z*<16
8zz*-4(z+z*)<16
8x2 +8y2 - 8x < 16
x2 +y2 - x < 2(x-½)2 +y2 < 2+½2
(x-½)2 +y2 < 9/4 ie(3/2)2Circle centre (½,0) radius 3/2
Real
Imaginary
Argand diagram|z-4| < | z-2i |
z+z*=2x and z-z* = 2yi
zz*-4z-4z*+16<zz*+2iz-2iz*+4
If z = x+yi then z* =x-yi
| z-4|2 < | z-2i |2
(z-4)(z*-4*) < (z-2i)(z*-2i*)
4z+4z*+2iz-2iz*>12
4(z+z*)+2i(z-z*)>12
8x +2i(2yi)> 12
2x - y > 3
8x +4yi2 > 128x -4y > 12
-2i*=2i
y<2x-3