Question

find the value of i^77​

Answer 1

✓ Answer

$= i$

✓ Solution

We know some values of complex numbers which are imaginary . They are :

${i}^{0} = 1$

${i}^{1} = i$

${i}^{2} = - 1$

${i}^{3} = - i$

${i}^{4} = 1$

We need to have these values so that it will be easy to solve sums related to Complex numbers.

Here they have asked value of an complex number , Lets find the value :

${i}^{77} = {i}^{4} \:^{19} \: \times {i}^{1}$

${i}^{77} = {1}^{19} \times i$

$\longrightarrow \: {i}^{77} = i$

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✓ Explanation :

» We know the value of i⁴ = 1

» So we took( i⁴) to the power 19

› Divide 77 by 4 ( the quotient value is 19 )

› Remainder is 1 ( i¹ ) = i

» Thereby we got i as the answer

For further information refer to the attachment !

Answer 2

Answer:

i

Step-by-step explanation:

if the power is odd then we have two options it can be i or -i so how do we know?

we subtract the power by 1, 77-1 = 76

then we divide it by 2, 76/2 = 38

it is even so it is going to be i

if it was odd number like 37 it was going to be -i