*Complex Numbers Multiplication Calculator* is an online tool for complex numbers arithmetic operation programmed to perform multiplication operation between two set of complex numbers. A complex number is an expression of the form a + bi, where a and b are real numbers. If z = a + bi is a complex number, then a and b are called the real part and imaginary part respectively of z, denoted Re(z) and Im(z). Complex numbers are used in many scientific fields, including engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory. So learning complex numbers arithmetic operation becomes necessary. Where the complex numbers multiplication calculator illustrate how complex numbers behave with respect to the basic multiplication operation corresponding to the real parts and imaginary parts. The multiplication between two complex numbers z_{1} and z_{2} can be derived from the formula

z_{1} = a + bj

z_{2} = c + dj

**Complex Numbers Multiplication Formula**

z_{1} . z_{2} = (a + bj).(c + dj)

= ac + adj + bcj +bdj^{2}

but remember j2 = -1,

So z_{1} . z_{2} = (ac - bd) + (bc + ad)j