Write the expression in the standard form $$ a+b i $$. $$ (-12+i)(-12-i) $$

Question

UpStudy AI · Accepted Answer

Given the expression
$$
(-12+i)(-12-i)
$$
we start by recognizing it as a product of two conjugates. Recall that for any numbers $$ a $$ and $$ b $$,
$$
(a+b)(a-b)=a^2-b^2.
$$
Here, $$ a=-12 $$ and $$ b=i $$. Therefore, we have:
$$
(-12+i)(-12-i)=(-12)^2-(i)^2.
$$

Calculating each term:
$$
(-12)^2=144
$$
and knowing that
$$
i^2=-1,
$$
we have:
$$
(i)^2=-1.
$$

Substitute these values:
$$
144-(-1)=144+1=145.
$$

Thus, the expression in standard form $$a+bi$$ is:
$$
145+0i.
$$
The expression in standard form is $$145 + 0i$$.

Write the expression in the standard form .

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions