pure 1

Question 1

9+-arg z in first quad

Answer 1

a

Question 2

arg z in second quad

Answer 2

pi-a

Question 3

arg z in third quad

Answer 3

-(pi-a)

Question 4

arg z in fourth quad

Answer 4

-a

Question 5

|z1z2|

Answer 5

|z1||z2|

Question 6

arg(z1z2)

Answer 6

argz1 + arg z2

Question 7

|z1/z2|

Answer 7

|z1|/|z2|

Question 8

arg (|z1/z2|)

Answer 8

argz1 - argz2

Question 9

1/a + 1/b

Answer 9

(a+b)/ab

Question 10

1/a + 1/b + 1/c

Answer 10

sum of doubles/abc

Question 11

1/a + 1/b + 1/c + 1/d

Answer 11

sum of triples / abcd

Question 12

a^n x b^n

Answer 12

(ab)^n

Question 13

a^n x b^n x c^n

Answer 13

(abc)^n

Question 14

a^n x b^n x c^n x d^n

Answer 14

(abcd)^n

Question 15

rule for sum of doubles

Answer 15

(sum of singles)^2 - 2)sum of doubles

Question 16

rule for sum of cubes

Answer 16

(sum of singles)^3 -3(sum singles)(sum doubles) +3(sum triples for cubics only)

Question 17

cartesian form of a vector line

Answer 17

(x-a1)/b1 = (y-a2)/b2 = (z-a3)/b3

Question 18

r.n=

Answer 18

a.n

Question 19

acute angle between 2 intersecting lines

Answer 19

cos z = |(a.b)/|a||b||

Question 20

acute angle between line and plane r.n=k

Answer 20

sin z = |(b.n)/|b||n||

Question 21

acute angle between two planes

Answer 21

cos z = |(n1.n2)/|n1||n2||

Question 22

volume about y axis

Answer 22

pi ⋅ integral x^2 dy

Question 23

volume about x axis

Answer 23

pi ⋅ integral y^2 dx

Question 24

when can two matrices be multiplied

Answer 24

number of columns in first matrix is equal to the number of rows in the second

Question 25

det of 2x2 matrix

Answer 25

ad-bc

Question 26

reflection in y axis

Answer 26

-1 0
0 1 invariant on y axis and lines x=0 y=k

Question 27

reflection in x axis

Answer 27

1 0
0 -1 invariant on x axis and lines y=0 x=k

Question 28

reflection in y=x

Answer 28

0 1
1 0 invariant on y=x and y=-x+k

Question 29

reflection in y=-x

Answer 29

0 -1
-1 0 invariant on y=-x and y=x+k