Multiply the complex conjugates. (2+9i)(2−9i) (1 point) Responses −77 negative 77 85 85 4+81i 4 plus 81 i 4−81i

Answer 1

To multiply the complex conjugates \((2 + 9i)(2 - 9i)\), we can use the formula for the product of complex conjugates, which is given by:

\[ (a + bi)(a - bi) = a^2 + b^2 \]

Here, \(a = 2\) and \(b = 9\).

Now we calculate:

\[ a^2 = 2^2 = 4 \] \[ b^2 = 9^2 = 81 \]

Therefore, the product is:

\[ a^2 + b^2 = 4 + 81 = 85 \]

Thus, the result of multiplying the complex conjugates \((2 + 9i)(2 - 9i)\) is \(85\).

So the final answer is \(\boxed{85}\).