Question

Evaluate the following:
$i + {i}^{3} + {i}^{5} + {i}^{7} + {i}^{9} + {i}^{11} + {i}^{13} + {i}^{15} + {i}^{17} + {i}^{19}$

Answer 1

According to laws of exponents,
if,
a^m×a^n = a^m+n
then,
a^m+a^n=a^m×n

So,
${i}^{3 \times 5 \times 7 \times 9 \times \times 11 \times 13 \times 15 \times 17 \times 19}$
${i}^{654,729,075}$
I hope it's correct.