pure 1 Flashcards
9+-arg z in first quad
a
arg z in second quad
pi-a
arg z in third quad
-(pi-a)
arg z in fourth quad
-a
|z1z2|
|z1||z2|
arg(z1z2)
argz1 + arg z2
|z1/z2|
|z1|/|z2|
arg (|z1/z2|)
argz1 - argz2
1/a + 1/b
(a+b)/ab
1/a + 1/b + 1/c
sum of doubles/abc
1/a + 1/b + 1/c + 1/d
sum of triples / abcd
a^n x b^n
(ab)^n
a^n x b^n x c^n
(abc)^n
a^n x b^n x c^n x d^n
(abcd)^n
rule for sum of doubles
(sum of singles)^2 - 2)sum of doubles
rule for sum of cubes
(sum of singles)^3 -3(sum singles)(sum doubles) +3(sum triples for cubics only)
cartesian form of a vector line
(x-a1)/b1 = (y-a2)/b2 = (z-a3)/b3
r.n=
a.n
acute angle between 2 intersecting lines
cos z = |(a.b)/|a||b||
acute angle between line and plane r.n=k
sin z = |(b.n)/|b||n||
acute angle between two planes
cos z = |(n1.n2)/|n1||n2||
volume about y axis
pi ⋅ integral x^2 dy
volume about x axis
pi ⋅ integral y^2 dx
when can two matrices be multiplied
number of columns in first matrix is equal to the number of rows in the second
det of 2x2 matrix
ad-bc
reflection in y axis
-1 0
0 1 invariant on y axis and lines x=0 y=k
reflection in x axis
1 0
0 -1 invariant on x axis and lines y=0 x=k
reflection in y=x
0 1
1 0 invariant on y=x and y=-x+k
reflection in y=-x
0 -1
-1 0 invariant on y=-x and y=x+k
