Imaginary number are based on the mathematical number $$ i $$.

$$ i \text is defined to be \sqrt-1 $$

From this 1 fact, we deserve to derive a basic formula for powers the $$ i $$ by feather at some examples.

Table 1$\text Table 1\\\beginarrayccc\hline Expression & & work & an outcome \\\hline\redi^ \textbf2 & = & ns \cdot ns = \sqrt-1 \cdot \sqrt-1 & \red \textbf -1 \\\hline\redi^ \textbf3 & = & i^2 \cdot i = -1 \cdot ns & \red \textbf-i \\\hline\red i^ \textbf4 & = & i^2 \cdot i^2 -1 \cdot -1 = & \red1\\\hline\endarray$

You should recognize Table 1 above .

Table 1 above boils down to the 4 conversions the you deserve to see in Table 2 below. You have to memorize Table 2 below because once you begin actually fixing problems, you"ll check out you use table 2 over and over again!

Table 2$\text Table 2$

exactly how to usage the pythagorean to organizeYou are watching: Simplify the number using the imaginary unit i.

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