Operations with Complex Numbers

The imaginary unit $$\text{i}$$ is defined as $$\text{i} = \frac{\text{sqrt}(-1)}{1}$$ .

The expression is already simplified as $$7 - 13i$$ .

The sum is $$7 - 3i$$ .

The product is $$10 + 10i$$ .

The product is $$-10 - 18i$$ .

A complex number is a number of the form $$a + bi$$ , where $$a$$ and $$b$$ are real numbers and $$i$$ is the imaginary unit.

The real part is $$3$$ .

The imaginary part is $$-2$$ .

In polar form, it is expressed as $$r(\text{cos}(\theta) + i\text{sin}(\theta))$$ , where $$r = \text{sqrt}(a^2 + b^2)$$ and $$\theta = \text{tan}^{-1}(\frac{b}{a})$$ .

The conjugate is $$3 - 4i$$ .