Argand Diagrams (AQA A-Level Further Maths): Flashcards

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Argand Diagrams
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Definition of Argand diagram

Plane for complex numbers: Re horizontal, Im vertical axes

Real axis on Argand diagram

Horizontal axis

Imaginary axis on Argand diagram

Vertical axis

How z=a+biz = a + bi is plotted on Argand diagram

As point (a,b)(a, b)

Complex conjugate of z=a+biz = a + bi

z=abiz^* = a - bi

Geometric property of zz^* on Argand diagram

Reflection of zz across real axis

Complex numbers represented as

Position vectors from origin to the point

Where kzkz lies for scalar kk and complex number zz

Straight line through origin and zz

Product of gradients of perpendicular lines

1-1

Horizontal position of z=a+biz = a + bi determined by

Real part aa

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