Complex Number Calculator

Used by the power and n-th roots operations.
Result (rectangular form)
11 - 2i
Complex Number Calculator
Real part of the result
11
Imaginary part of the result
-2
Modulus of the result
11.18034
Argument of the result (radians)
-0.179853
Argument of the result (degrees)
-10.304846
Polar form
11.18034 (cos -10.304846 deg + i sin -10.304846 deg)
Exponential form
11.18034 e^(-0.179853 i)
Conjugate of the result
11 + 2i
What was computed
(a) x (b)
Worked out from NIST Digital Library of Mathematical Functions, Chapter 4: Elementary Functions and 1 other source.

How this is worked out

5 steps
  1. a = 3 + 4i (modulus 5, argument 53.130102 deg)
  2. b = 1 - 2i (modulus 2.236068, argument -63.434949 deg)
  3. (x + yi)(u + vi) = (xu - yv) + (xv + yu)i
  4. Result = 11 - 2i
  5. |result| = sqrt(11^2 + -2^2) = 11.18034

Results are general information, not financial, tax, legal, medical or engineering advice.