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

$$-3i$$ .

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

$$7 - 3i$$ .

To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and remember that i^2 = -1.

$$-6$$ .

$$-15$$ .

The conjugate of a complex number a + bi is a - bi. It is used to simplify the division of complex numbers.