Complex numbers Flashcards
How to add two complex numbers which are in modulus argument form?
Multiply their modulus’s and add their arguments. Do the opposite for division.
What region must the principle argument lie within?
theta should be between 0 and 2pi.
What is the geometrical effect of multiplying a complex number by another in modulus argument form?
The initial line enlarges by scale factor r and is rotated through angle theta anticlockwise.
How do you represent a circle using complex numbers?
|z-a|=r.Where a is the centre and r is the radius.
How do you represent a half line?
arg(z-a)=theta.Half line starting at a making angle theta with x axis.
How do you represent a perpendicular bisector between two points?
|z-a|=|z-b|.The line is a perpendicular bisector between point a and point b.Find the line by solving the two complex numbers.
How to represent features not part of the locus?
Use dotted lines to represent them
What is the formula de moivere’s theorem.
r^n(cosntheta+isinntheta)=(r(costheta+isintheta))^n
What is omega representing?
The smallest positive argument when k=1.
How to express cosntheta in terms of cos theta?
(Costheta+isintheta)^n then equate real parts.
How to convert cos^n theta in terms of multiple angles?
use identity cosntheta=z^n+z^-n/2 for sin use z^n-z^-n/2i.
What is the eponential identity for cos and sin?
cos=e^ithetha+e^-itheta/2.Sin numerator sin switch and divide by 2i.
