complex numbers Flashcards
1
Q
What is the set of complex numbers?
A
C = {x + iy : x, y ∈ R}
2
Q
how do you add complex nums
A
add real and imaginary individually
3
Q
how does multiplication work
A
(x+iy)·(a+ib) = (xa−yb)+i(xb+ya),
4
Q
what is the complex conjugate
A
the conjugate of x + iy = x - iy
5
Q
What is the modulus of z
A
(x^2 + y^2)^(1/2)
6
Q
What is Z multiplied by its conjugate
A
The square of modulus z
7
Q
What is the polar form
A
(Where O = theta,)
r(cos(O) + iSin(O)) = z
where r = modulus z
and O = the angle measured from the positive real axis, until it reaches the point mapped by the complex number
8
Q
A
