Adding and Subtracting Complex Numbers page 11

Arithmetic Operations on Complex Numbers

• Arithmetic operations can be performed on complex numbers in a manner similar to real numbers.

• To add or subtract complex numbers, combine the real parts together and combine the imaginary parts together.

General Formulas for Addition and Subtraction

• Formula for adding complex numbers:   $(a + bi) + (c + di) = (a + c) + (b + d)i$

• Formula for subtracting complex numbers:   $(a + bi) - (c + di) = (a - c) + (b - d)i$

Step-by-Step Procedure to Find the Sum or Difference

• Given two complex numbers, follow these steps to calculate their sum or difference:

  1. Identify the real and imaginary parts of each complex number.

  2. Add or subtract the real parts.

  3. Add or subtract the imaginary parts.

Example: Adding Complex Numbers

• Problem statement: Add $3 - 4i$ and $2 + 5i$.

• Step-by-step resolution:

  • Step 1: Identify the real and imaginary parts of each complex number.

  • First number $3 - 4i$: Real part = $3$, Imaginary part = $-4$

  • Second number $2 + 5i$: Real part = $2$, Imaginary part = $5$

  • Step 2: Add the real parts:     $3 + 2 = 5$

  • Step 3: Add the imaginary parts:     $-4 + 5 = 1$

  • Combine the results into standard complex form:     $(3 - 4i) + (2 + 5i) = (3 + 2) + (-4 + 5)i = 5 + 1i = 5 + i$