Question

determine o valor de

a) i^10 + i^13 - i^22

b) i^72 + i^11

Answer 1

i=√-1

i²=-1

i³=i²*i =-i

i⁴=-i*i=-1 *(-1)=1

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a) i^10 + i^13 - i^22 =(i²)⁵+i*(i⁴)³ -(i²)¹¹=(-1)⁵+i*(1)³ -(-1)¹¹=-1+i+1=i 

b) i^72 + i^11 =(i²)³⁶ +i* i¹⁰ =(-1)³⁶ +i*(i²)⁵ =1 +i*(-1)⁵ =1 - i