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- Arithmetic operations with complex numbers

This solver can performs basic operations with complex numbers i.e., **addition, subtraction,
multiplication** and **division**. Step-by-step explanations are provided.

example 1:

$$\left( 2 - 4i \right) \color{red}{+} \left(5 + 3i\right)$$

example 2:

$$\left( \frac{1}{2} - 2i \right) \color{red}{\cdot} \left(\frac{5}{2} - \frac{6}{5}i\right)$$

example 3:

$$\frac{4-6i}{1+i}$$

example 4:

$$\left( \frac{7}{2} - 2i \right) \color{red}{-} \left(\frac{5}{2} + 3i\right)$$

A complex numbers are of the form , ** a+bi** where

For addition, add up the real parts and add up the imaginary parts.

**Example:** let the first number be *2 - 5i* and the second
be *-3 + 8i*. The sum is:

**
(2 - 5i) + (- 3 + 8i) =
= ( 2 - 3 ) + ( -5 + 8 ) i
= - 1 + 3 i **

Subtract the real parts and subtract the imaginary parts.

**Example:** let the first number be *-3 + 7i* and the second
be *6 - 9i*. The sum is:

**
(- 3 + 7i) - (6 - 9i) =
= ( - 3 - 6 ) + ( 7 - ( -9 ) ) i
= - 9 + 16 i **

To multiply complex method use the **FOIL method**( **F**irst, **O**utside, **I**nside,
and **L**ast. )

**Example:** multiply **3 + 4i** and **2 - 6i**

**First terms:** 3 * 2 = 6

**Outside terms:** 3 * (- 6i) = -18i

**Inside terms:** 4i * 2 = 8i

**Last terms:** 4i * (-6i) = -24 * i^{2} =
-24 (- 1) = 24

Now, combine everything together

6 - 18i + 8i + 24 = 30 - 10i.

Multiply both the denominator and the numerator by the conjugate of the denominator

**Example: ** divide **2 + 3i** and **4 - 5i**

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