Question 394183
the expression i<sup>42</sup> is equivalent to ?
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You need to know these three facts:

i<sup>2</sup> = -1

(-1)<sup>EVEN</sup> = +1

(-1)<sup>ODD</sup> = -1

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Your example:

i<sup>42</sup> = i<sup>2*21</sup> = (i<sup>2</sup>)<sup>21</sup> = (-1)<sup>21</sup> = -1

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Some other examples:

i<sup>96</sup> = i<sup>2*48</sup> = (i<sup>2</sup>)<sup>48</sup> = (-1)<sup>48</sup> = +1 = 1

i<sup>73</sup> = i<sup>72+1</sup> = i<sup>72</sup>i<sup>1</sup> = i<sup>2*36</sup>i = (i<sup>2</sup>)<sup>36</sup>i = (-1)<sup>36</sup>i = 1i = i

i<sup>47</sup> = i<sup>46+1</sup> = i<sup>46</sup>i<sup>1</sup> = i<sup>2*23</sup>i = (1<sup>2</sup>)<sup>23</sup>i = (-1)<sup>23</sup>i = (-1)i = -i

Edwin</pre>