complex numbers Flashcards
areas of chemistry complex numbers comes up in
wavefunctions
X-ray scattering calculations
refractive index
what is a closed sum
you have integer plus integer gets and integer
what is a rational number
all fractions proper improper negative and all integers
what is an irrational number
cannot be expressed by terminating or repeating decimal no pattern identified
what is root -1
i
what is root -9
root -1 times root9
so plus minus 31
what are possible values of i^m when m is an integer
i, -1, -i, 1
then it cycles again
what is i^-1
-1
what is i^0
1
equation for a complex nummber and what the different parts mean
z = x + iy
x is the real part of z
y is the imaginary part of z
what is a pure imaginary number
z = iy
where are complex numbers
it is a point on the complex plane z = x + iy
what is the complex
conjugation of z
z*
x - iy
cartesian representation
polar representation of a complex number
rcostheta + i r sintheta or r(costheta + isintheta)
when are complex numbers equal
when their real and imaginary parts are equal
how to do sums with imaginary numbers
just as if the real numbers are real and the imaginary ones are a number coefficient of x in brackets
how to solve complex numbers dividing
times both numerator and denominator by the second complex number but with a negative sign to move complex off bottom of fraction
how many roots does a quadratic equation have
2 real roots if discriminant bigger than 0
1 repeated root if discriminant equal to 0
a pair of complex roots z and z*
