(-1+6i)^2

2 min read Jun 16, 2024
(-1+6i)^2

Squaring a Complex Number: (-1 + 6i)^2

This article will explore the process of squaring the complex number (-1 + 6i).

Understanding Complex Numbers

Complex numbers are expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Squaring a Complex Number

To square a complex number, we simply multiply it by itself:

(-1 + 6i)^2 = (-1 + 6i) * (-1 + 6i)

Expanding the Expression

We can expand this product using the distributive property (or FOIL method):

(-1 + 6i) * (-1 + 6i) = (-1)(-1) + (-1)(6i) + (6i)(-1) + (6i)(6i)

Simplifying the Expression

Simplifying the terms, we get:

1 - 6i - 6i + 36i^2

Since i^2 = -1, we can substitute it into the expression:

1 - 6i - 6i + 36(-1)

Combining the real and imaginary terms:

1 - 36 - 6i - 6i = -35 - 12i

Conclusion

Therefore, the square of the complex number (-1 + 6i) is -35 - 12i.

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