Solutions to Review Problems for Midterm III
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6 = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Let rk = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Therefore r0 = 2(cos( π 6 )+i sin( 6 )) = √ 3+i, r1 = 2(cos( π 2 )+i sin( 2 )) = 2i, r2 = 2(cos( 5π 6 )+ i sin( 6 )) = − √ 3 + i, r3 = 2(cos( 7π 6 ) + i sin( 6 )) = − √ 3 − i, r4 = 2(cos( 2 ) + i sin( 2 )) = −2i and r5 = 2(cos( 6 ) + i sin( 11π 6 )) = √ 3 − i. So the roots of
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Solutions to Review Problems for Midterm III
6 = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Let rk = 2(cos( (π+2kπ) 6 ) + i sin( (π+2kπ) 6 )) where k = 0, 1, 2, · · · , 5. Therefore r0 = 2(cos( π 6 )+i sin( 6 )) = √ 3+i, r1 = 2(cos( π 2 )+i sin( 2 )) = 2i, r2 = 2(cos( 5π 6 )+ i sin( 6 )) = − √ 3 + i, r3 = 2(cos( 7π 6 ) + i sin( 6 )) = − √ 3 − i, r4 = 2(cos( 2 ) + i sin( 2 )) = −2i and r5 = 2(cos( 6 ) + i sin( 1...
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