IB Maths AI 1.10 Definitions

This page contains our IB Maths AI definitions for 1.10. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Advanced complex numbers'.

All Topic 1 Sub-topics 1.1: Scientific Notation 1.2: Arithmetic Sequences 1.3: Geometric Sequences 1.4: Interest 1.5: Introduction To Exponents & Logs 1.6: Handling Numbers 1.7: Use Of Technology (HL)1.8: Advanced exponents & logs (HL)1.9: Introduction to complex numbers (HL)1.10: Advanced complex numbers (HL)1.11: Introduction to matrices (HL)1.12: Advanced matrices

amplitude

The distance from the principal axis to a maximum or minimum of a sinusoidal graph, given by '

\left|a\right|

Argand

A diagram where a complex number

a+bi

is plotted as the point

(a,b)

, with the real part on the horizontal axis and the imaginary part on the vertical axis.

argument

The angle a complex number makes with the positive real axis on an Argand diagram; for

z=r\operatorname{cis}\theta

, it is

\arg\left(z\right)=\theta

cis

Shorthand for

\cos\theta+i\sin\theta

, so a complex number in polar form can be written as

z=r\operatorname{cis}\theta

conjugate

The complex number obtained by changing the sign of the imaginary part; if

z=a+bi

then

\overline{z}=a-bi

, which reflects the point in the real axis on an Argand diagram.

frequency

A table that shows how often each value (discrete) or each class interval (continuous) occurs.

multiplication

An operation on complex numbers that, in polar form, multiplies moduli and adds arguments: if

z_1=r_1\operatorname{cis}\theta_1

and

z_2=r_2\operatorname{cis}\theta_2

, then

z_1z_2=r_1r_2\operatorname{cis}\left(\theta_1+\theta_2\right)

phase

The angle that determines the horizontal shift of a sinusoidal function; in

a\cos\left(\omega t+\alpha\right)

it is

\alpha

phasors

Complex-number representations of sinusoidal functions with a fixed frequency, where the modulus gives the amplitude and the argument gives the phase angle.

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