Complex numbers Definitions Conversions Arithmetic Hyperbolic Functions.

Presentation on theme: "Complex numbers Definitions Conversions Arithmetic Hyperbolic Functions."— Presentation transcript:

Complex numbers Definitions Conversions Arithmetic Hyperbolic Functions

Main page Argand diagram Im Re If the complex number then the Modulus of is written as and the Argument of is written as so that are shown in the Argand diagram If then the conjugate of, written or is If then is the real part of and is the imaginary part Define the imaginary number so that Complex numbers: Definitions

Cartesian form (Real/Imaginary form) Polar form (Modulus/Argument form) Exponential form Im Re Main page Principal argument If is the principal argument of a complex number then Im Re Polar to Cartesian form Cartesian to Polar form NB. You may need to add or subtract to in order that gives in the correct quadrant Eulers formula Complex numbers: Forms

Addition/ subtraction Multiplication Equivalence Let and Division Polar/ exponential form: Mult/division If and then and Main page De Moivres theorem Polar/ exponential form: Powers/ roots If then and Complex numbers: Arithmetic

Hyperbolic Sine & Cosine Functions Main page Equivalences Eulers formula Sine & Cosine Functions in Exponential form Other Hyperbolic Functions Complex numbers: Hyperbolic Functions

Main page Complex numbers Thats all folks!