Math Calculators, Lessons and Formulas
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This solver can performs basic operations with complex numbers i.e., addition, subtraction, multiplication and division. Step-by-step explanations are provided.
A complex numbers are of the form , a+bi where a is called the real part and bi is called the imaginary part. This text will show you how to perform four basic operations (Addition, Subtraction, Multiplication and Division):
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( First, Outside, Inside, and Last. )
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 * i2 = -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