Adding and Subtracting Complex Numbers and Powers of i

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^2 = -1.

The imaginary unit 'i' is defined as the square root of -1, i.e., i = $$\frac{{\text{sqrt}(-1)}}{{1}}$$ .

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

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

The result is -5 + 7i.

The result is 2 + 4i.

The result is -38 + 45i.

The result is 19 + 6i.

The result is 7 - 13i.

The conjugate of a complex number a + bi is a - bi.