Complex Roots

Question 1

Fundamental Theorem of Algebra

Answer 1

Every complex polynomial can be written as a series of linear factors.

Corollary: a polynomial of odd degree has at least on real zero.

Question 2

Conjugate Pairs Theorem

Answer 2

Complex / imaginary roots come in pairs.

When two conjugates multiply together, the middle term always cancels out.

Question 3

Complex numbers are:

Answer 3

Real numbers
And
Non-real numbers

Question 4

The imaginary number i = ?

Answer 4

The square root of -1

Question 5

What does i ^2 = ?

Answer 5

(Square root of -1) x (Square root of -1)

= -1

Question 6

i ^3 = ?

Answer 6

i x i ^2 =

(Square root of -1) x (-1) = the negative square root of -1 or -i

Question 7

Shortcuts

\+/-i 
\+/-2i
\+/-3i
\+/-4i
\+/-10i

Answer 7

(x+i)(x-i)= x^2+1

(x+2i)(x-2i)= x^2+4

(x-3i)(x+3i)= x^2+9

(x-4i)(x+4i)= x^2+16

(x+10i)(x-10i)= x^2+100