Answer :
To simplify the expression
[tex]$$
(8-5 i)^2,
$$[/tex]
we can start by using the formula for the square of a binomial:
[tex]$$
(a-b)^2 = a^2 - 2ab + b^2.
$$[/tex]
In our case, [tex]$a = 8$[/tex] and [tex]$b = 5i$[/tex]. Now, let's compute each term step by step.
1. Calculate [tex]$a^2$[/tex]:
[tex]$$
8^2 = 64.
$$[/tex]
2. Calculate [tex]$-2ab$[/tex]:
[tex]$$
-2 \cdot 8 \cdot 5i = -80i.
$$[/tex]
3. Calculate [tex]$b^2$[/tex]:
[tex]$$
(5i)^2 = 25i^2.
$$[/tex]
Remember, [tex]$i^2 = -1$[/tex], so:
[tex]$$
25i^2 = 25 \times (-1) = -25.
$$[/tex]
4. Combine the results for the real and imaginary parts:
For the real part:
[tex]$$
64 + (-25) = 39.
$$[/tex]
The imaginary part remains:
[tex]$$
-80i.
$$[/tex]
Thus, the final result is:
[tex]$$
(8-5i)^2 = 39 - 80 i.
$$[/tex]
[tex]$$
(8-5 i)^2,
$$[/tex]
we can start by using the formula for the square of a binomial:
[tex]$$
(a-b)^2 = a^2 - 2ab + b^2.
$$[/tex]
In our case, [tex]$a = 8$[/tex] and [tex]$b = 5i$[/tex]. Now, let's compute each term step by step.
1. Calculate [tex]$a^2$[/tex]:
[tex]$$
8^2 = 64.
$$[/tex]
2. Calculate [tex]$-2ab$[/tex]:
[tex]$$
-2 \cdot 8 \cdot 5i = -80i.
$$[/tex]
3. Calculate [tex]$b^2$[/tex]:
[tex]$$
(5i)^2 = 25i^2.
$$[/tex]
Remember, [tex]$i^2 = -1$[/tex], so:
[tex]$$
25i^2 = 25 \times (-1) = -25.
$$[/tex]
4. Combine the results for the real and imaginary parts:
For the real part:
[tex]$$
64 + (-25) = 39.
$$[/tex]
The imaginary part remains:
[tex]$$
-80i.
$$[/tex]
Thus, the final result is:
[tex]$$
(8-5i)^2 = 39 - 80 i.
$$[/tex]
