5.5 1) 1 cos(π4) +i sin(π4)
= √22 +√22 i 2) 2 cos(π) +isin(π)
= 2 (−1 +i·0) = 2·(−1) =−2 3) √
2 cos(π6) +i sin(π6)
=√ 2 √
3 2 +12i
= √26 + √22i
4) 12 cos(54π) +i sin(54π)
= 12
−
√2
2 +i(−
√2 2 )
=−
√2
4 −
√2 4 i
5) 2 cos(76π) +i sin(76π)
= 2
−
√3
2 +i(−
1 2)
=−
√3−i
6) √
3 cos(73π) +i sin(73π)
=√ 3
1 2 +i
√3 2
= √23 + 32i
Algèbre : nombres complexes — forme trigonométrique Corrigé 5.5