Working with 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^2 = -1.

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

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.

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

The product of two complex conjugates (a + bi)(a - bi) is a^2 + b^2.

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

To multiply two complex numbers (a + bi)(c + di), use the distributive property: ac + adi + bci + bdi^2, and simplify using i^2 = -1.

The real part of a complex number a + bi is the value 'a'.

The imaginary part of a complex number a + bi is the value 'b'.

The result is $$1 - 8i$$ .