Chapter 2 Introduction To Complex Numbers Flashcards
What is the form of complex numbers?
Complex numbers are of the form z = x + yi with i^2= -1
What is the real part and imaginary part of a complex number?
x is called the real part, Re(z), and y is called the imaginary part, Im(z).
What is the conjugate of a complex number z = x + yi?
The conjugate of z = x + yi is
z = x - yi.
How do you add or subtract complex numbers?
To add or subtract complex numbers, add or subtract the real and imaginary parts separately.
How do you multiply complex numbers?
To multiply complex numbers, expand the brackets then simplify using (x1 + y1i)(x2 + y2i) = (x1x2 - y1y2) + (x1y2 + x2y1)i.
How do you divide complex numbers?
To divide complex numbers, write as a fraction, then multiply top and bottom by the conjugate of the bottom and simplify the answer.
When are two complex numbers equal?
Two complex numbers Z1 = x1 + y1i and Z2 = x2 + y2i are equal if and only if x1 = x2 and y1 = y2.
What is an Argand diagram?
The real/imaginary axes system is known as an Argand diagram.
