Mathematics: Match each of the following complex numbers with its equivalent expression.i^110 i^92i^245i^347-i-1i1 arrowbotharrowbotharrowbotharrowboth

Match each of the following complex numbers with

Ответ:

dondre54

15.01.2022

Mathematics

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

$i^{110}=-1$

$i^{92}=1$

$i^{245}=i$

$i^{347}=-i$

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Ответ:

jordanrose98

27.05.2022

Mathematics

Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.

Step-by-step explanation:

Have. A. Good. Day. ༼ つ ◕_◕ ༽つ♥️

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

i^110

i^92

i^245

i^347

-i
-1
i
1

arrowboth

arrowboth

arrowboth

arrowboth

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