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Simplifying complex numbers

There are a surprising number of consequences to the fact that $i^2 = -1$, and one of these is how far one can simplify a complex number. Indeed, it is always possible to put any complex number into the form $a + b\cdot i$, where $a$ and $b$ are real numbers. This is not always obvious, however there is a set technique to accomplish that task. As usual we start with demonstrating the technique in a general case, and then give a concrete example for one to use in comparison.

As we saw above, any (purely) numeric expression or term that is a complex number, can always be reduced using this technique to the form $A + Bi$ where $A$ and $B$ are some real numbers. Because of this, we say that the form $A + Bi$ is the “standard form” of a complex number.

1 : Simplify the following complex expression into standard form.
2 : Simplify the following complex expression into standard form.
3 : Simplify the following complex expression into standard form.
4 : Simplify the following complex expression into standard form.