Question

Evaluate the following:
i) $i^{-888}$
ii) $i^{30}+i^{40}+i^{50}+i^{60}$

Answer 1

As we know that

${i}^{4} = 1$
$1) i^{-888} \\ \\ = \frac{1}{ {i}^{888} } \\ \\ = \frac{1}{ { ({i}^{4} )}^{222} } \\ \\ = \frac{1}{ {1}^{222} } \\ \\ = \frac{1}{1} \\ \\ i^{-888} = 1$
$2) i^{30}+i^{40}+i^{50}+i^{60} \\ \\ i^{7 \times 4 + 2}+i^{4 \times 10}+i^{4 \times 12 + 2}+i^{4 \times 15} \\ \\ = {i}^{4 \times 7} {i}^{2} + 1 + {i}^{2} + 1 \\ \\ = {i}^{2} + 1 + {i}^{2} + 1 \\ \\ = - 1 + 1 - 1 + 1 \\ \\ i^{30}+i^{40}+i^{50}+i^{60} = 0$
Hope it helps you.

Answer 2

Answer:

I) 1

ii) 0

Step-by-step explanation:

i hope this helps you