Question

- any idea about this please ... ?

,,a mathematical expression in "i" can have real value " ?

Answer 1

\[\sqrt{- 1} = i\]

Answer 2

or \[i^{2} = - 1 \]

Answer 3

Do you want a answer to both of them?

Answer 4

both of what ?

Answer 5

both or the expressions

Answer 6

\[\sqrt{-1} = i \]

\[i^{2} = - 1 \]

so these i ve wrote to be clarified about what ,,i" i talk ...

Answer 7

So what do you know about this?

Answer 8

about what ?

Answer 9

,,mathematical expression" ?

-- look pls on definition of a mathematical expression

Answer 10

Definition: Mathematical Expression

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

Answer 11

`operations such as addition, subtraction, multiplication, division, exponentiation`
but which one is used for this question

Answer 12

this is a general question ?

Answer 13

oh

Answer 14

for example :

\[\left( e^{i}/(i + 3\right) = x , x \in R\]

Answer 15

or something in this way ...

Answer 16

so this question i ve got in the past night here where now is 15,17 PM Sunday and i ve get that an expression in ,,i" to have real value in R - what i ve thought till today that not possibile ...

Answer 17

15:17 pm?
is that army time or,,,

Answer 18

no

i live in Central Europe and here this is the actual time

Answer 19

ty but no

i ve wrote these

\[\sqrt{-1} = i \]

and

\[i^{2} = - 1 \]

just to be clarified about what ,,i" i talk

Answer 20

Are you just asking if both of those i equations are true?

Answer 21

no

pls read what i ve wrote above

Answer 22

I'm still confused what you are tryna ask...

Answer 23

\(\color{#0cbb34}{\text{Originally Posted by}}\) @stuyou
What is ve?
\(\color{#0cbb34}{\text{End of Quote}}\)
it was `I've` but he didnt put the apostrophe I think

Answer 24

yes exactly

Answer 25

ty @Laylalyssa

Answer 26

oh np

Answer 27

Bw the above two equations that u gave we gotta choose one?

Answer 28

no

these are just examples about what ,,i" i talk

Answer 29

but i ve wrote there an expression in i for example too

Answer 30

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
for example :

\[\left( e^{i}/(i + 3\right) = x , x \in R\]
\(\color{#0cbb34}{\text{End of Quote}}\)
this ...

Answer 31

@Mercury opinion ? pls.

Answer 32

i have no idea sorry

Answer 33

@jhonyy9 I didn't get your point exactly.
Do you want to ask why iota brings out to real solution, righr?

Answer 34

Oh I get it, he's asking if it's possible to formulate an expression with 'i' where the result is ALWAYS a real number.

Answer 35

i^2 is real
i^4 is real
i^6 is real

so how about i^2x where x is an integer?

\[i^{2x} = y,y \in R,x \in Z\]

Answer 36

not exactly

suppose there is an expression for example what i ve wrote above

(e^i/(i+3)=x , x∈R

so this is possibile ? an expression with ,,i" so to have real root(s) ?

Answer 37

` A mathematical expression in "i" can have real value`

Why not !

Try this,
\[\large \bf (2+i)(2-i) \in R\]

Answer 38

Moreover, `not every complex number expression leads to a real value`

Answer 39

\(\color{#0cbb34}{\text{Originally Posted by}}\) @loveboy
` A mathematical expression in "i" can have real value`

Why not !

Try this,
\[\large \bf (2+i)(2-i) \in R\]
\(\color{#0cbb34}{\text{End of Quote}}\)
where is the variable of x ?

Answer 40

\[\large \bf (2+i)(2-i) = x\]

Solve for x

Answer 41

Tell me, what you get ?

Answer 42

on the left side there is formula a^2 -b^2

Answer 43

Right, go ahead

Answer 44

-2i +2i eliminate

Answer 45

this is very simple

Answer 46

i ve said about expression where i remain there dont eliminate

Answer 47

See, if you consider `i` in an expression, that leads to an imaginary expression and imaginary expression has imaginary roots, therefore, not real.

Answer 48

for example

\[\frac{ 2\ln i }{ i } = x , x \in R\]

solve it for x

Answer 49

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
for example

\[\frac{ 2\ln i }{ i } = x , x \in R\]

solve it for x
\(\color{#0cbb34}{\text{End of Quote}}\)

The expression you wrote is an imaginary number, therefore, not any chance has real roots.
(illustration in graph above)

Answer 50

no

i ve said above (2ln i )/i = x

can can be real ?

Answer 51

\(\color{#0cbb34}{\text{Originally Posted by}}\) @loveboy
\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
for example

\[\frac{ 2\ln i }{ i } = x , x \in R\]

solve it for x
\(\color{#0cbb34}{\text{End of Quote}}\)

The expression you wrote is an imaginary number, therefore, not any chance has real roots.
(illustration in graph above)
\(\color{#0cbb34}{\text{End of Quote}}\)
yeah i ve thought it the same but i can prove it that exist x be real

Answer 52

Prove it !

Answer 53

sorry this is my idea about this so i will include it in my book what i will write in the near future

Answer 54

but for you get anything about this proof so you need use the Euler's formula

Answer 55

You're talking about to evaluate to `pi`, right ?

Answer 56

not really

Answer 57

Great! Best of luck :)

Answer 58

ty