Complex Number Operations Calculator

Enter a and bi piece:

a =  bi =

Enter c and di piece:

c =  di =
              

How does the Complex Number Operations Calculator work?

Free Complex Number Operations Calculator - Given two numbers in complex number notation, this calculator:
1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.
2) Determines the Square Root of a complex number denoted as √a + bi
3) Absolute Value of a Complex Number |a + bi|
4) Conjugate of a complex number a + bi
This calculator has 4 inputs.

What 6 formulas are used for the Complex Number Operations Calculator?

a + bi + (c + di) = (a + c) + (b + d)i
a + bi - (c + di) = (a - c) + (b - d)i
(a * c) + (b * c) + (a * d) + (b * d)
The square root of a complex number a + bi, is denoted as root1 = x + yi and root2 = -x - yi
|a + bi| = sqrt(a2 + b2)
a + bi has a conjugate of a - bi and a - bi has a conjugate of a + bi.

For more math formulas, check out our Formula Dossier

What 8 concepts are covered in the Complex Number Operations Calculator?

absolute value
A positive number representing the distance from 0 on a number line
addition
math operation involving the sum of elements
complex number
a number that can be written in the form a + b or a - bi
complex number operations
conjugate
A term formed by changing the sign between two terms in a binomial.
division
separate a number into parts
multiplication
math operation involving the product of elements
subtraction
math operation involving the difference of elements

Example calculations for the Complex Number Operations Calculator

  1. sqrt6+i
  2. sqrt(5+3i)
  3. square root(8+7i)
  4. square root -2+6i
  5. (2 + 3i)(9 - 8i)
  6. (9 - 6i)*(2 - 4i)
  7. (5 - 7i)/(7 + 3i)
  8. Absolute value 3 + 4i
  9. abs(6 - 8i)
  10. |8 - 5i|
  11. 8/3 + 4i
  12. conjugate of 9-4i
  13. 2i, 3



Complex Number Operations Calculator Video