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<p><span style="font-weight: bold; color: #003300;">Calcula les següents potències de la unitat imaginària, i:</span><br style="font-weight: bold; color: #003300;" /><br style="font-weight: bold; color: #003300;" /><span style="font-weight: bold; color: #003300;">a. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«/mstyle»«/math» </span><br style="font-weight: bold; color: #003300;" /><br style="font-weight: bold; color: #003300;" /><span style="font-weight: bold; color: #003300;">b. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/mstyle»«/math» </span><br style="font-weight: bold; color: #003300;" /><br style="font-weight: bold; color: #003300;" /><span style="font-weight: bold; color: #003300;">c. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«/mstyle»«/math» </span><br style="font-weight: bold; color: #003300;" /><br style="font-weight: bold; color: #003300;" /><sup style="font-weight: bold; color: #003300;">d. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/msup»«/mstyle»«/math» </sup></p>
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Answer 1
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
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Answer 2
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
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100%
50%
33.33333%
25%
20%
10%
0%
Hint 1
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<p><span style="color: #000080;"><strong>Com que les potències de i es repeteixen, </strong></span></p> <p><span style="color: #000080;"><strong>i<sup>4·q+r</sup> = i<sup>4·q</sup> · i<sup>r</sup> = 1 · i<sup>r</sup></strong></span></p> <p><span style="color: #000080;"><strong>Cal doncs fer la divisió entera de la potència per 4.</strong></span></p> <p><span style="color: #000080;"><strong>El residu de la divisió de #a per 4 és #r1, per això «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»s«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»o«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»l«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math»</strong></span></p> <p> </p>
Hint 2
Hint text
<p><span style="color: #000080;"><strong>El residu de la divisió de #b per 4 és #r2</strong></span></p> <p><span style="color: #000080;"><strong>El residu de la divisió de #c per 4 és #r3</strong></span></p> <p><span style="color: #000080;"><strong>El residu de la divisió de #d per 4 és #r4</strong></span></p>
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