Powers of i and Complex Numbers

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as i = √(-1).

The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to extend the real number system to complex numbers.

The complex number -2 + 5i is located in Quadrant II.

The complex number 3 - 4i can be represented as the point (3, -4) in the complex plane.

The complex number 4i is located on the Y-Axis.

The distance from the origin to point B (5, 0) is 5.

The distance from the origin to point A (3, 4) is $$\text{d} = \text{sqrt}(3^2 + 4^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5$$ .

The modulus of a complex number z = a + bi is given by |z| = $$\text{sqrt}(a^2 + b^2)$$ .

The conjugate of a complex number z = a + bi is given by z* = a - bi.

To add two complex numbers, add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.