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