Multiplicating Complex Numbers Calculator

A Complex Number is expressed in the form of a + bi where a, b are real numbers and i is the imaginary part. In the given expression a is the real part and b is the imaginary part of the complex number. Complex Number extends the concept of one-dimensional line to a two-dimensional complex plane and uses the horizontal axis for the real part and vertical axis for the imaginary part.

We know the expansion (a+b)(c+d)=ac+ad+bc+bd

Similarly, consider the complex numbers z₁ = a₁+ib₁ and z₂ = a₂+ib₂

Product of z₁z₂ is defined as

z₁z₂ = (a₁+ib₁)(a₂+ib₂)

z₁z₂=a₁a₂+a₁b₂i+b₁a₂i+b₁b₂i²

we know the value of i² is -1

z₁z₂=(a₁a₂-b₁b₂)+i(a₁b₂+a₂b₁)

For any non-zero complex number z=a+ib(a≠0 and b≠0) there exists another complex number z^-1 or 1/z which is known as the multiplicative inverse of z such that zz^-1=1

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