Imaginary Number Calculator

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The arithmetic operation to apply to z1 and z2.
The real part of the first complex number z1 = a + bi.
The imaginary part of the first complex number z1 = a + bi.
The real part of the second complex number z2 = c + di.
The imaginary part of the second complex number z2 = c + di.
Result in rectangular form
5 - i

Full result written as a + bi

Result (real part)5
Result (imaginary part)-1
Result modulus |z|5.099
Result argument (deg)-11.31deg
Result in polar form5.09902(cos(-11.31 deg) + i sin(-11.31 deg))
z1 modulus |z1|3.6056
z1 argument (deg)33.69deg
z1 conjugate3 - 2i
z2 modulus |z2|1.4142
z2 argument (deg)-45deg
z2 conjugate1 + i
Result real part5
Result imaginary part-1
Result modulus5.099

Result of multiplied: 5 - i

  • The result has both a real part (5.0000) and an imaginary part (-1.0000i).
  • Its modulus is 5.0990, the distance from the origin in the complex plane.
  • The argument is -11.31 degrees, measured anticlockwise from the positive real axis.

Next stepMultiplication rotates z1 by the argument of z2 and scales its modulus by |z2|. Try polar form to see this geometrically.

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