Perform the indicated operations. Write the answer in standard form, $$ a+b i $$. $$ (\sqrt{10}+\sqrt{6} i)(\sqrt{10}-\sqrt{6} i)=\square $$

Question

UpStudy AI · Accepted Answer

We are given
$$
(\sqrt{10}+\sqrt{6}\, i)(\sqrt{10}-\sqrt{6}\, i).
$$

Notice that these are complex conjugates. The product of a complex number and its conjugate is given by
$$
(a+bi)(a-bi)=a^2+b^2.
$$

Here, $$ a=\sqrt{10} $$ and $$ b=\sqrt{6} $$. Thus, we have

$$
(\sqrt{10})^2+(\sqrt{6})^2 = 10 + 6 = 16.
$$

We can write $$16$$ in standard form as

$$
16+0 i.
$$
The answer is $$16 + 0i$$.

Perform the indicated operations. Write the answer in standard form, \( a+b i \). \[ (\sqrt{10}+\sqrt{6} i)(\sqrt{10}-\sqrt{6} i)=\square \]