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Imaginary unit

With a 2×2-matrix you can write the imaginary unit i as

In this matrix, the imaginary unit i itself is not present.

 

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Explanation

You can describe the complex number z = a + bi by

and therefore you get for the imaginary unit

 

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Example 1

We calculate i² = –1 with a matrix multiplication

and this corresponds with the definition of the imaginary unit.

 

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