Operations with Complex Numbers
To add two complex numbers, add the real part to the real part and the imaginary part to the imaginary part.
Example:
(2 + 7i) + (3 – 4i) = (2 + 3) + (7 + (–4))i
= 5 + 3iTo subtract two complex numbers, subtract the real part from the real part and the imaginary part from the imaginary part.
Example:
(9 + 5i) – (4 + 7i) = (9 – 4) + (5 – 7)i
= 5 – 2i
To multiply two complex numbers, use the FOIL method and combine like terms.
Example:
(3 + 2i)(5 + 6i) = 15 + 18i + 10i + 12i2
= 15 + 28i – 12
= 3 + 28i
To divide two complex numbers, multiply the numerator and denominator by the complex conjugate, expand and simplify. Then, write the final answer in standard form.
Example:
