Question

Simplify the expression to a + bi form: (-1-2i)^2

Answer 1

-3 + 4i

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Apply the square of a sum identity:

• (a + b)² = a² + 2ab + b²

Substituting -1 for a and -2i for b, we have:

• (-1)² + 2(-1)(-2i) + (-2i)²

Which simplifies to:

• 1 + 4i + 4i²

Since i² = -1, the expression further simplifies to:

• 1 + 4i - 4

Finally, we combine like terms to get the final result:

• -3 + 4i