Addition and subtraction of complex numbers

In this publication, we will consider formulas with which you can find the sum or difference of two complex numbers presented in algebraic form. Examples are also given for a better understanding of the theoretical material.

Addition of complex numbers

If you add two complex numbers x = a₁ + b₁i и y = to₂ + b₂i, then we get a complex number z:

z = x + y = (a₁ + a₂) + (b₁ + b₂) ⋅ i

Thus, we separately add the real and imaginary parts of the summed numbers.

Example 1

Let’s find the sum of complex numbers: x = 8 + 3i и y = 5 – i.

Decision:

x + y = (8 + 5) + (3i – i) = 13 + 2i.

Subtraction of complex numbers

Difference of two complex numbers x = a₁ + b₁i и y = to₂ + b₂i calculated by the formula:

z = x – y = (a₁ – and₂) + (b₁ – b₂) ⋅ i

That is, you get a complex number, the real and imaginary parts of which are equal to the difference of the corresponding parts x и y.

Example 2

Subtract from x = 12 – 7i number y = -8 + 4i.

Decision:

x – y = (12 – (-8)) + (-7i – 4i) = 20 – 11i.