complex numbers

Question 1

areas of chemistry complex numbers comes up in

Answer 1

wavefunctions
X-ray scattering calculations
refractive index

Question 2

what is a closed sum

Answer 2

you have integer plus integer gets and integer

Question 3

what is a rational number

Answer 3

all fractions proper improper negative and all integers

Question 4

what is an irrational number

Answer 4

cannot be expressed by terminating or repeating decimal no pattern identified

Question 5

what is root -1

Answer 5

i

Question 6

what is root -9

Answer 6

root -1 times root9

so plus minus 31

Question 7

what are possible values of i^m when m is an integer

Answer 7

i, -1, -i, 1

then it cycles again

Question 8

what is i^-1

Answer 8

-1

Question 9

what is i^0

Answer 9

1

Question 10

equation for a complex nummber and what the different parts mean

Answer 10

z = x + iy
x is the real part of z
y is the imaginary part of z

Question 11

what is a pure imaginary number

Answer 11

z = iy

Question 12

where are complex numbers

Answer 12

it is a point on the complex plane z = x + iy

Question 13

what is the complex

conjugation of z

Answer 13

z*
x - iy
cartesian representation

Question 14

polar representation of a complex number

Answer 14

rcostheta + i r sintheta
or r(costheta + isintheta)

Question 15

when are complex numbers equal

Answer 15

when their real and imaginary parts are equal

Question 16

how to do sums with imaginary numbers

Answer 16

just as if the real numbers are real and the imaginary ones are a number coefficient of x in brackets

Question 17

how to solve complex numbers dividing

Answer 17

times both numerator and denominator by the second complex number but with a negative sign to move complex off bottom of fraction

Question 18

how many roots does a quadratic equation have

Answer 18

2 real roots if discriminant bigger than 0
1 repeated root if discriminant equal to 0
a pair of complex roots z and z*