Complex Numbers Flashcards
1
Q
i
A
√-1
2
Q
i^2
A
-1
3
Q
i^3
A
-i
4
Q
i^4
A
1
5
Q
i^5
A
i
6
Q
How do you add and subtract complex numbers?
A
Use same rules as you would in algebra
7
Q
How do you multiply complex numbers?
A
Expand brackets like you would in algebra, remembering i^2 = -1
8
Q
How do you divide complex numbers?
A
Like you would surds, so rationalising the denominator technique
9
Q
How do you √ complex numbers?
A
Say √ of your complex number = a+bi
Square both sides
Equate real and imaginary parts (so a^2 - b^2 = and 2ab = )
Substitute a and b back into a+bi, not forgetting conjugates
10
Q
Modulus Complex Number
A
Distance from the origin on an Argand Diagram, found using Pythagoras’ theorem
11
Q
What does z’s Modulus Complex Number equal?
A
z* Modulus Complex Number
