Simplify the expression to a + bi form:

left parenthesis, minus, 11, plus, i, right parenthesis, squared

(−11+*i*)2

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 \(i\).

Simplify the expression to a + bi form: (−11 + i)²

Simplify the expression (-11 + i)² into a + bi form by using binomial expansion and properties of complex numbers. This detailed solution breaks down the process and is suitable for students in Grades 10-12. Learn how to work with complex numbers and key algebraic formulas.

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