Question

the value of i109 is​

Answer 1

109/4= 27 remainder 1

Using above knowledge

i109=

(i4)27×i1=

(1)27×i1=

1×i1=

i1=

i

Answer 2

Correct question is "Find the value of ${i}^{109}$".

Answer:

Required value of the given term is i .

Step-by-step explanation:

Given,${i}^{109}$

We want to find value of the given term.

Now,

${i}^{109} \\ = {i}^{100 + 9} \\ = {i}^{100} \times {i}^{9} \\ = { {i}^{2} }^{50} \times {i}^{ {3}^{3} } \\ = {( - 1)}^{50} \times {( - i)}^{3} \\ = 1 \times i \\ = i$

Here applied formula,

${i}^{2} = - 1 \\ {i}^{3} = - i$

${a}^{x} \times {a}^{y} = {a}^{x + y}$

This is a problem of complex number of Algebra.

Some important Algebra's formulas:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

Two more important Algebra's problem:

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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