This equation shows the relationship between the most fundamental imaginary number, \( \htmlClass{sdt-0000000129}{j} \), and the real numbers.
\( j \) | This symbol represents the imaginary unit, which is defined as the square root of \(-1\). \( j = \sqrt{-1}\). It is the most fundamental unit in the field of complex numbers, allowing for the expression of numbers that cannot be represented on the real number line. |
\( (5 + \htmlClass{sdt-0000000129}{j})^2 \) can be rewritten to be
\[ (5 +\htmlClass{sdt-0000000129}{j})(5 + \htmlClass{sdt-0000000129}{j}) \]
This is equivalent to...
\[ 5 \cdot 5 + 5 \cdot \htmlClass{sdt-0000000129}{j} + 5 \cdot \htmlClass{sdt-0000000129}{j} + \htmlClass{sdt-0000000129}{j}^2 \]
This simplifies to...
\[25 + 10 \htmlClass{sdt-0000000129}{j} + \htmlClass{sdt-0000000129}{j}^2\].
We can now use our identity, to get...
\[25 + 10 \htmlClass{sdt-0000000129}{j} - 1\]
which simplifies to...
\[24 + 10 \htmlClass{sdt-0000000129}{j}\]