(1-i)^4 In A+ib Form

Jasonbradley

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Jun 16, 2024

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Finding the Complex Number (1 - i)^4 in the Form a + ib

This article will guide you through the process of calculating the complex number (1 - i)^4 and expressing it in the form a + ib.

Understanding Complex Numbers

A complex number is a number that can be expressed in the form a + ib, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Calculating (1 - i)^4

To find (1 - i)^4, we can use the following steps:

1. Expand the expression: (1 - i)^4 = (1 - i)^2 * (1 - i)^2 We can calculate (1 - i)^2 first: (1 - i)^2 = (1 - i)(1 - i) = 1 - i - i + i^2 = 1 - 2i - 1 = -2i

2. Substitute and multiply: (1 - i)^4 = (-2i)(-2i) = 4i^2 = 4(-1) = -4

3. Express in a + ib form: Since -4 is a real number, we can write it as -4 + 0i.

Conclusion

Therefore, (1 - i)^4 expressed in the form a + ib is -4 + 0i.