Where's the denominator
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 4: Multiply the denominators.
We are multiplying $(-4-5i)$ by its conjugate $(-4+5i)$. This follows the form $(a-bi)(a+bi) = a^2 + b^2$.
Here, $a=-4$ and $b=5$.
$$ (-4-5i)(-4+5i) = (-4)^2 - (5i)^2 $$
$$ = 16 - (25i^2) $$
Substitute $i^2 = -1$:
$$ = 16 - 25(-1) $$
$$ = 16 + 25 $$
$$ = 41 $$
The denominator is $\boxed{41}$.
