Simplify Imaginary Numbers

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as $$i = \frac{\text{sqrt}(-1)}{1}$$ .

The value of $$i^2$$ is -1.

$$5i$$ .

$$i\sqrt[]{14}$$ .

$$3i\sqrt[]{2}$$ .

$$i\sqrt[]{5}$$ .

Real numbers can be represented on a number line, while imaginary numbers are represented on a perpendicular axis, forming the complex plane.

A complex number is a number that can be expressed in the form $$a + bi$$ , where $$a$$ is the real part and $$b$$ is the imaginary part.

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

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