COMPLEX NUMBERS

What is an imaginary number?

Imaginary number is the number i, number which is not real.

i² = -1

i = (square root) of -1.

What is a complex number?

A number defined in the form of x + iy.

x and y are real values

i is the unit imaginary number

How do we denote a complex number?

We use the letter z. z = x + iy

What are the real parts and imaginary parts of a complex number?

x - real part of z, denoted by Re z

y - imaginary part of z, denoted by Im z

When are two complex numbers equal?

When their real parts are equal and when their imaginary parts are equal.

What is the complex conjugate of z = x + iy ?

z* = x - iy

How would we divide (8 - i)/(2 + 3i)?

We would multiply the whole fraction with the conjugate of 2 + 3i. That means we would divide with (2 - 3i)/(2 - 3i).

How can a complex number be reresented on a complex plane?

The x-axis is the real axis Re(z)

The y-axis is the imaginary axis Im(z).

What is the Cartesian form?

When a complex number is written in the form of z = x + iy.

What is the modulus of a complex number?

That is the magnitude of the position vector.

/z/ = (square root) of (x² + y²)

What is the argument of a complex number?

That is the direction of the position vector.

Actually it is the angle made between the positive real axis and the position vector.

Argument is given in radians, arg z.

How do we find the argument?

tan theta = y/x