XX Test 2 (3, 5)

Question 1

always for Cartesian form , write…

Answer 1

+ 0i

0 + ni

Question 2

when solving for roots of unity (or roots in general), always write 2 things

Answer 2

where k is an integer
by de Moivre

Question 3

how to prove a quad is a parallelogram?

Answer 3

1 pair of equal parallel sides

or

2 pairs of parallel sides

Question 4

Division Theorem

Answer 4

Question 5

(Fundamental Theorem of Algebra)
All polynomials with real coefficients of an odd degree must have

Answer 5

at least one real root

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

vector equation for circles/spheres

Answer 9

Question 10

with vector equations of lines, what’s b?

Answer 10

b is the position vector of a fixed point B, on the line

B IS GIVEN POINT

Question 11

vector equation of a line through the origin

Answer 11

Question 12

vector equation of a line through a given point

Answer 12

Question 13

conditions for intersections of lines in 2d planes

Answer 13

lines must be parallel

Question 14

Answer 14

Question 15

Answer 15

Question 16

find vector equation of the line y = 4x

Answer 16

Question 17

Answer 17

Question 18

how to find intersection of 2 lines

Answer 18

Question 19

if a complex number is a root of a polynomial with real coefficients, then

Answer 19

the conjugate is also a root

Question 20

vector equation of a line through 2 given points

Answer 20

Question 21

how to get equation of line segment?

Answer 21

Question 22

lines in vector form are parallel if…

Answer 22

their direction vectors are parallel

Question 23

lines in vector form are perpendicular if

Answer 23

their direction vectors are perpendicular AND if they intersect!!!!

Question 24

cot 90 = and why?

Answer 24

0
cotθ = cosθ/sinθ
= cos90/sin90
= 0/1
=
0

Question 25

for a quartic

sum of roots

sum of the product of 2 roots

sum of the product of 3 roots

product of roots

Question 26

for a quadratic
sum of roots
product of roots

Answer 26