Question

Match each of the following complex numbers with its equivalent expression.

i^110

i^92

i^245

i^347

-i
-1
i
1






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Answer 1

Answer: Y

Explanation:

Answer 2

Therefore

`i^(110)=-1`

`i^(92)=1`

`i^(245)=i`

`i^(347)=-i`

Explanation:

Complex Number :

A complex number is a number that can be expressed in the form

`a + bi`

where a and b are real numbers, and

' i ' is called an imaginary number.

The value of i is given as

`i=√(-1)`

Squaring both the side we get

`i^(2)=(√(-1))^(2)\\\therefore i^(2)=-1`

Therefore on substituting we get

For i^110

`i^(110)=(i^(2))^(55)=(-1)^(55)=-1`

Similarly for i^92

`i^(92)=(i^(2))^(46)=(-1)^(46)=1`

Similarly for i^245

`i^(245)=(i^(2))^(122)* i=(-1)^(122)* i=1* i =i`

Similarly for i^347

`i^(347)=(i^(2))^(173)* i=(-1)^(173)* i=-1* i =-i`

Therefore

`i^(110)=-1`

`i^(92)=1`

`i^(245)=i`

`i^(347)=-i`