Question

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

Answer 1

Answer:

Therefore

$i^{110}=-1$

$i^{92}=1$

$i^{245}=i$

$i^{347}=-i$

Step-by-step 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

$i=\sqrt{-1}$

Squaring both the side we get

$i^{2}=(\sqrt{-1})^{2}\\\therefore i^{2}=-1$

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

$i^{245}=(i^{2})^{122}\times i=(-1)^{122}\times i=1\times i =i$

Similarly for i^347

$i^{347}=(i^{2})^{173}\times i=(-1)^{173}\times i=-1\times i =-i$

Therefore

$i^{110}=-1$

$i^{92}=1$

$i^{245}=i$

$i^{347}=-i$