Question

what is iota to the power 10(i^10)???​

Answer 1

Step-by-step explanation:

we know the formula

i^(4k+2)=i

for any integer k

so, if k=2 we get that,

i^10 which is equal to i

or root -1

Answer 2

i¹⁰ = - 1

Given :

The expression i¹⁰

To find :

Simplify the given expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is i¹⁰

Step 2 of 2 :

Simplify the given expression

We know that " i " is the complex number satisfying the property i² = - 1

Thus we get

$\displaystyle \sf{ {(i)}^{10} }$

$\displaystyle \sf{ = {(i)}^{(2 \times 5)} }$

$\displaystyle \sf{ = {( {i}^{2} )}^{5} \: \: \: \bigg[ \: \because \: {( {a}^{m} )}^{n} = {a}^{mn} \: \bigg] }$

$\displaystyle \sf{ = {( - 1)}^{5} }$

$\displaystyle \sf{ = - 1 }$

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