Unit 2 Flashcards
1
Q
How do you simplify complex number division?
A
Multiply both parts of the fraction by the conjugate of the denominator to eliminate the imaginary numbers
2
Q
How do you multiply Polar Form complex numbers?
A
Multiply the moduli and add the arguments
3
Q
How can trigonometric and hyperbolic functions be related?
A
cosh jx = cos x sinh jx = j sin x tanh jx = j tan x cos jx = cosh x sing jx = j sinh x tan jx = j tanh x
4
Q
How do you find the nth root of z?
A
Put the modulus to the nth root
Add 2πk to the angle and divide by n, where k is an integer from 0 -> n-1
5
Q
What is (Z-x-jy) equivalent to?
A
Z translated from the origin to point (x,y) on the argand diagram
6
Q
What are the direction cosines?
A
l = cosA = x/r m = cosB = y/r n = cosC = z/r
7
Q
What is the sum of squares of the direction cosines?
A
1
8
Q
What does a dot product of 0 mean?
A
The lines are perpendicular
9
Q
What is the angle between two 3D vectors, a & b?
A
a.b/mod(a)*mod(b)
