what is iota in qudratic equation answer in detail and other new related terms like iota in other lessons"
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It. ( iota) is the ninth letter of the Greek alphabet .. and it is generally denoted by the letter 'i' ...
And it represents.. the complex number... √-1
we get complex roots for an equation when d ( B²- 4 ac) in an equation is less than 0...
ex of equation ...
X²+x+2=0
here b = 1 , a = 1 , c = 2
by applying B²- 4ac we get..
1² - 4 x 1 x 2 ... which is less than 0... ie complex roots ..
Hope you understood what iota denotes..
And it represents.. the complex number... √-1
we get complex roots for an equation when d ( B²- 4 ac) in an equation is less than 0...
ex of equation ...
X²+x+2=0
here b = 1 , a = 1 , c = 2
by applying B²- 4ac we get..
1² - 4 x 1 x 2 ... which is less than 0... ie complex roots ..
Hope you understood what iota denotes..
john44:
please tell some other related different terms like it in other lessons
you will also get OMEGA .. as a term... it is denoted by 'w'
i think it is in physics so please make me familiarise with some other more terms
all the terms like alpha , beta , gama... are greek alphabets .. usually denote variables .. and another one like ' theta' this greek letter mostly denotes angles
you can even take SIGMA or SUMMATION into consideration too... summation is basically sum of terms..
and PI .. this PI looks like the normal pi ( 3.14) but is written bigger in size ... and represents product of terms
pls mark as Brainliest bro..
bro .. Brainliest ?
thx man
np
Answered by
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iota is a Greek word . it is denoted by" i "
value of i = √(-1)
actually when quadratic equation don't give real zeros or roots then we use concept of complex number in which iota take important role .
example :-
x² +x +2 =0 what is its roots ????
you solve by quadratic formula,
e.g x = { -b±√(b² -4ac)}/2a
x ={ -1±√(1-8)}/2
here you see in square root negative number is coming .then here there are no real roots exist .
but we put √(-7) =√(-1)(7) =√7i
now, this gives roots of given quadratic
e.g x = { -1±i√7} /2
in the same way ,
x² +1 =0
x² = -1
x= ±√(-1)
=± i
x = -i , and + i are the roots of given quadratic .
property of iota :-
========================
from above we know ,
i = √(-1)
take square both sides
i² = -1
hence, i² = -1
i³= i²i = (-1)i = -i
i⁴ =(I)² (I)² =(-1)(-1)= 1
hence,
# i = √(-1)
# i²= -1
# i³ =-i
# i⁴ = 1
I will not give more explanation , because you read this in detail complex number . I hope this will helpful .
value of i = √(-1)
actually when quadratic equation don't give real zeros or roots then we use concept of complex number in which iota take important role .
example :-
x² +x +2 =0 what is its roots ????
you solve by quadratic formula,
e.g x = { -b±√(b² -4ac)}/2a
x ={ -1±√(1-8)}/2
here you see in square root negative number is coming .then here there are no real roots exist .
but we put √(-7) =√(-1)(7) =√7i
now, this gives roots of given quadratic
e.g x = { -1±i√7} /2
in the same way ,
x² +1 =0
x² = -1
x= ±√(-1)
=± i
x = -i , and + i are the roots of given quadratic .
property of iota :-
========================
from above we know ,
i = √(-1)
take square both sides
i² = -1
hence, i² = -1
i³= i²i = (-1)i = -i
i⁴ =(I)² (I)² =(-1)(-1)= 1
hence,
# i = √(-1)
# i²= -1
# i³ =-i
# i⁴ = 1
I will not give more explanation , because you read this in detail complex number . I hope this will helpful .
thanks its enough for now for me thanks
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