Comments

Addition and subtraction of complex numbers in algebraic form


Addition

Considering the complexes:

,

the sum is obtained by summing its real and imaginary parts separately:

= (a + c) + (b + d) i

Examples

  • (2 + 3i) + (5 + 4i) = (2 + 5) + (3 + 4) i = 7 + 7i
  • 2i + (6 + 9i) = (0 + 6) + (2 + 9) i = 6 + 11i
  • (5 + 3i) + 3 = (5 + 3) + (3 + 0) i = 8 + 3i

Subtraction

Given the complexes ,
the difference is obtained by subtracting its real and imaginary parts separately:

= (a - c) + (b - d) i


Examples

  • (2 + 3i) - (5 + 4i) = (2 - 5) + (3 - 4) i = -3 - i
  • 2i - (6 - 9i) = (0 - 6) + (2 - (- 9)) i = -6 + 11i
  • (5 + 3i) - 3 = (5 - 3) + (3 - 0) i = 2 + 3i
Next: Multiplication and Division in Algebraic Form