Complex numbers

Question 1

What is the imaginary number?

Answer 1

Square root of a negative number
i^2 = -1
i= square root -1

Question 2

Why i?

Answer 2

1. Alegbra
2. Easy way of expressing and manipulating sinusoidal quantities
3. Signal processing - 1D and 2D Fourier Transforms

1D = EEG, Magnetic Resonance Spectroscopy, Ultrasound

2D = MRI - k space

Question 3

What is the standard form of complex numbers?

Answer 3

z= a + bi

a+b = real numbers
i = imaginary number

Question 4

What are complex numbers?

Answer 4

Orthogonal

Question 5

What is the equation of addition of complex number?

Answer 5

(a+c)+(b+d)i

Question 6

What is the equation of multiplication of complex number?

Answer 6

(ac-bd)+(ad+bc)i

Question 7

What is the complex conjugate?

Answer 7

z=a-bi

rule applies only to complex number expressed in STANDARD FORM

Question 8

How do you make a real number?

Answer 8

Multiply a complex number by its conjugate

Question 9

How can vector R be represented on Cartesian plane?

Answer 9

R = xi + yj

Question 10

What is magnitude of vector R?

Answer 10

square root x^2 + y^2

Question 11

What is Argand Diagram?

Answer 11

Orthogonal cartesian axes i and j replaced by orthogonal Real and Imaginary axes in complex plane

Question 12

What is the argument of z ?

Answer 12

angle theta

Tan-1 (b/a)

Question 13

What can be reached by a unit vector r?

Answer 13

Any point on a unit circle

r= cos(theta)i+sin(theta)j

Question 14

What is Euler’s formula?

Answer 14

Z=e^i(theta)

Question 15

What is the polar form?

Answer 15

z=re^i(theta)