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Square

Every complex number is a square, because

where r is the modulus of the complex number.

 

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Explanation

Take a complex number a + bi. The number  is called r. It applies

   so      and   

We now calculate

For b ≥  0 this gives

 

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Example 1

To calculate the square root of the imaginary unit we substitute a = 0 and b = 1 in the formula

From r² = a² + b² follows r = 1 and you get

We take the square root on both sides

 

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