To simplify the expression $(−11+i)^2$ to the form $a + bi$, we can expand it using the formula for the square of a binomial:

$(a + b)^2 = a^2 + 2ab + b^2$

In this case, $a = -11$ and $b = i$, so:

$(-11 + i)^2 = (-11)^2 + 2(-11)(i) + (i)^2$

Now, calculate each term:

1. $(-11)^2 = 121$
2. $2(-11)(i) = -22i$
3. $(i)^2 = -1$ (since $i^2 = -1$)

Now, combine these results:

$(-11 + i)^2 = 121 - 22i - 1$

Simplify further:

$(-11 + i)^2 = 120 - 22i$

So, the simplified expression in $a + bi$ form is:

$120 - 22i$

Would you like details or have any questions?

Here are 5 related questions:

1. How would you expand and simplify $(3 - 4i)^2$?
2. What is the magnitude of the complex number $120 - 22i$?
3. How do you add two complex numbers, such as $5 + 2i$ and $3 - i$?
4. What is the square root of a complex number like $-1 + i$?
5. How can you express the complex number $120 - 22i$ in polar form?

Tip: When working with complex numbers, always remember that $i^2 = -1$. This key property allows you to simplify powers and products involving $i$.