Complex Numbers

Question 1

What is i

Answer 1

square root of -1

Question 2

(z-a)(z-b)=

Answer 2

z^2 -(a+b)z + ab = 0

Question 3

What can be used to check the root types eg real or imaginary

Answer 3

The discriminant b^2 - 4ac

Question 4

What could be the products of a quadratic equation

Answer 4

2 real
2 imaginary

Question 5

What could be the products of a cubic equation

Answer 5

3 real
2 imaginary 1 rel

Question 6

What could be the products of a quartic equation

Answer 6

2 real 2 imaginary
4 real
2 pairs of imaginary

Question 7

What is a conjugate pair

Answer 7

when the two equation have the same numbers but opposing symbols
a + bi and a - bi

Question 8

What are the different forms of complex numbers

Answer 8

a + bi
z = r(cos* + isin*)
r = e^ i x pi x *

Question 9

How would you show sin n*

Answer 9

1. use demoivres theorem
2. use 1st year binomial expansion
3. collate like terms
4. substitute in cos+sin =1 to change values
   and collect terms

Question 10

What is demoivres theorem

Answer 10

z ^n = r^n (cos n* + isin n*)

Question 11

z equation for sin*

Answer 11

z - 1/z = sin*

Question 12

z equation for cos*

Answer 12

z + 1/z = cos*

Question 13

What is eulers equation

Answer 13

e^i x pi +1 = 0

Question 14

Key trig and complex equations

Answer 14

cos* = 1/2 (e^ipi + e^-ipi)
sin* = 1/2i (e^ipi - e^-ipi)

Question 15

If it is an n sided shape then what is the angle

Answer 15

2pi / n