Question

Simply
i^3+i^20
show work

Answer 1

the answer is 1-i


so, the order is i -1 -i 1.

if you have an exponent of 1, the answer is i.

if you have an exponent of 2, the answer is -1.

if you have an exponent of 3, the answer is -i.

if you have an exponent of 4, the answer is 1.

if you have an exponent of 5, the answer is i.

this repeats in this pattern. so one way to solve it is to count, or you can simply divide the exponent by 4.

if the answer has .25, it’s i.
if the answer has .50, it’s -1.
if the answer has .75, it’s -i.
if the answer has a whole nunber, any, such as 4 or 7, it’s 1.

3/4=.75. so i^3= -i.
20/4= 5. so i^20=1.
(-i) + (1) = 1-i

Answer 2

Answer: 1 - i

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Step-by-step explanation:

Recall that

i = sqrt(-1)

Squaring both sides gets us

i^2 = -1

Now let's multiply both sides by i

i*i^2 = i*(-1)

i^3 = -i

Repeat the last step

i^3 = -i

i*i^3 = i*(-i)

i^4 = -i^2

i^4 = -(-1)

i^4 = 1

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Here's a summary so far

• i^0 = 1
• i^1 = i
• i^2 = -1
• i^3 = -i
• i^4 = 1

The pattern repeats every 4 items. This means we'll divide the exponent by 4 and look at the remainder.

20/4 = 5 remainder 0

Therefore i^20 = i^0 = 1

Or we can think of it like this

i^20 = (i^4)^5 = 1^5 = 1

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This means we can then say

i^3 + i^20 = -i + 1 = 1 - i