Imaginary Numbers

The value is $$i$$ , which is the imaginary unit.

The simplified expression is 5i.

The value is $$3i\sqrt{2}$$ .

The value is $$-1$$ .

The value is $$1$$ .

Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit $$i$$ , where $$i = \sqrt{-1}$$ .

Real numbers can be represented on a number line, while imaginary numbers cannot; they exist on a separate axis in 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.

To multiply complex numbers, use the distributive property and remember that $$i^2 = -1$$ .