Answer:
First question: answer is d. 4) -i
[tex] {i}^{16} + {i}^{6} - 2 {i}^{5} + {i}^{13} \\ = ( {i}^{2} ) {}^{8} + ( {i}^{2} ) {}^{3} - 2( {i}^{2} )( {i}^{2})(i) + ( {i}^{5} ) {}^{ \frac{13}{5} } \\ = {( - 1)}^{8} + {( - 1)}^{3} - 2(1i) + ( - 1) {}^{ \frac{13}{2} } \\ = 1 - 1 - 2i + i \\ = - i[/tex]
Second question: answer is d. 4) 0
[tex] = {i}^{99} - {i}^{3} \\ =( {i}^{3} )( {i}^{96} ) - {i}^{3} \\ = {i}^{3} ( ({i {}^{2} )}^{48} - 1) \\ = - i(1 - 1) \\ = 0[/tex]
