Online tool Multiplying Complex Numbers Calculator is programmed to perform multiplication operation of complex numbers and gives the result in no time. All you need to do is enter the complex numbers and tap on the enter button to get the product of complex numbers.

**Ex:** (2+2i)(4+4i) or (4+2i)(4+4i) or (2+2i)(4+4i)(4+4i)

**Multiplying Complex Numbers Calculator:**Complex Numbers are used in many fields and you need to multiply them at times. Get to know the basic multiplication operation related to real and imaginary parts of the Complex Number explained in detail here. Read more to know more about What is Complex Number and how to find multiplication of Complex Numbers, etc.

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 z_{1} = a_{1}+ib_{1} and z_{2} = a_{2}+ib_{2}

Product of z_{1}z_{2} is defined as

z_{1}z_{2} = (a_{1}+ib_{1})(a_{2}+ib_{2})

z_{1}z_{2}=a_{1}a_{2}+a_{1}b_{2}i+b_{1}a_{2}i+b_{1}b_{2}i^{2}

we know the value of i^{2} is -1

z_{1}z_{2}=(a_{1}a_{2}-b_{1}b_{2})+i(a_{1}b_{2}+a_{2}b_{1})

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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**1. What is the Product of two Complex Numbers?**

The Product of two Complex Numbers is also a Complex Number.

**2. What happens if you multiply a complex number with its conjugate?**

If you multiply a complex number with its conjugate the answer is always a real number.

**3. How do you multiply Complex Numbers on a Calculator?**

You just need to give the input values i.e. complex numbers and tap on the enter button to get the product of numbers.

**4. What is the Product or Multiplication of Complex Numbers (2+2i) and (4+4i)?**

Given Complex Numbers are (2+2i) and (4+4i)

As per the formula

z_{1}z_{2}=a_{1}a_{2}+a_{1}b_{2}i+b_{1}a_{2}i+b_{1}b_{2}i^{2}

Multiply as per the formula

Product = (2+2i)*(4+4i)

=2.4+2.4i+4.2i+2i.4i

= 8+8i+8i+8i^{2}

we know the value of i^{2} = -1

= 8+16i+8(-1)

=8+16i-8

= 16i

Therefore, the product of Complex Numbers (2+2i) and (4+4i) is 16i