Question

could you find the product of the given complex number and its conjugate: 3-9i

Answer 1

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Product of complex numbers

Complex numbers are expressed in the form:

$Z=a+\mathbf{i}b$

Where i is the base of the imaginary numbers:

$\mathbf{i}=\sqrt[]{-1}$

We must recall that

$i^2=-1$

We have to find the product of:

$(3+9\mathbf{i})((3-9\mathbf{i})$

Multiply term by term:

$(3+9\mathbf{i})(3-9\mathbf{i})=9-27\mathbf{i}+27\mathbf{i}-81i^2$

Since i squared is -1:

$(3+9\mathbf{i})(3-9\mathbf{i})=9+81=90$

Thus, the product of the complex is a real number and it's equal to 90