To simplify the expression $(−11−10i)^2$, follow the process of squaring a complex number.

Step 1: Write the expression

$(-11 - 10i)^2$

Step 2: Use the formula for squaring a binomial

$(a + b)^2 = a^2 + 2ab + b^2$ In this case:

• $a = -11$
• $b = -10i$

Now apply the formula: $(-11 - 10i)^2 = (-11)^2 + 2(-11)(-10i) + (-10i)^2$

Step 3: Calculate each term

1. $(-11)^2 = 121$
2. $2(-11)(-10i) = 220i$
3. $(-10i)^2 = (-10)^2 \times i^2 = 100 \times (-1) = -100$

Step 4: Add the results together

$121 + 220i - 100 = 21 + 220i$

Final Answer:

$(−11−10i)^2 = 21 + 220i$

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5 Related Questions:

1. How do you multiply two complex numbers?
2. What is the general form of a complex number?
3. How do you find the conjugate of a complex number?
4. How do you divide complex numbers?
5. What is the magnitude of a complex number?

Tip:

When squaring a complex number, always remember that $i^2 = -1$.