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What is (−5 − 𝑖)²?

What is negative five minus 𝑖 all squared?

To square the complex numbers shown, we need to multiply it by itself. We need to multiply negative five minus 𝑖 by negative five minus 𝑖. One way to distribute the parentheses or expand the brackets here is to use the FOIL method. Multiplying negative five by negative five gives us 25. Multiplying the outside terms gives us five 𝑖. The inner or inside terms also have a product of five 𝑖. Multiplying the last terms gives us 𝑖 squared. Negative five minus 𝑖 multiplied by negative five minus 𝑖 is equal to 25 plus five 𝑖 plus five 𝑖 plus 𝑖 squared.

From our knowledge of imaginary numbers, we know that 𝑖 squared is equal to negative one. 25 minus one is equal to 24, and five 𝑖 plus five 𝑖 is equal to 10𝑖. This means that negative five minus 𝑖 all squared is equal to 24 plus 10𝑖.

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