awn786 2 years ago What is the square root of minus 1. When i do it in a scientific calculator, it says 'i' (imaginary unit) and i have no idea what that means

1. awn786

$\sqrt{-1} = x$ what is the value of x

2. awn786

3. zaynahf

Imaginary numbers result when you are taking the square root of any negative number: For an example, $\sqrt{-1}$ = i $\sqrt{-25} = 5i$ The 'i' is kind of like the negative sign

4. awn786

so what is an imaginary unit

5. zaynahf

I know of a video you can watch if you want to

6. awn786

yes what is the vid @zaynahf

7. hba

did you see the link @awn786 It has everything.

8. awn786

yes i did but what is an imaganary unit

9. zaynahf
10. awn786

WOW OMG complicated @hba

11. zaynahf

The first link is really straight forward, try that

12. hba

@awn786 Well,I tried to simplify and put everything :)

13. awn786

thanks for trying. @hba

14. hba

You are welcome :)

15. awn786

listen and can u give a simple i word answer: $\sqrt{-1}=x$ what is the value of x in numbers.

16. awn786

17. awn786

not i word

18. hba

I can help you understand what imaginary numbers are. So,the base of imaginary numbers is actually laid upon some of the things like $\huge \ i=\sqrt{-1}$ The other thing is $\huge\ \omega=\frac{ -1+i \sqrt{3} }{ 2 }$

19. awn786

whats w

20. hba

We call this omega,It's derivations is given in my link :)

21. awn786

whats w @hba

22. hba

Now as per your question. x=root{-1} x=i Here i is actually iota and it is an imaginary number.

23. hba

That's omega @awn786

24. awn786

whats omega

25. hba

26. awn786

27. hba

Well,In numbers it is sqrt{-1}

28. awn786

it should be easy shouldent it.

29. awn786

30. awn786

what is omega

31. hba

I have already told you what omega is.

32. awn786

no u havent @hba

33. hba

I said it is -1+i sqrt{3}/2

34. awn786

ok (i dont get it but ok) i' only in year 9 doing my gcse's

35. GCR92

$\sqrt{-1}$ doesn't exist as a the REAL number you are asking for, because there's no number that you can square (because of the SQUARE root) and gives you -1

36. GCR92

you just need to know what a square root is

37. awn786

i know what a square root is ofc

38. GCR92

that's why there's no sqrt of ANY negative numbers, because everthing squared is BIGGER than 0

39. GCR92

(possitive)

40. awn786

oh i get it so its an imaganary number because it cant exist?

41. awn786

you have the best responce

42. GCR92

EXACTLY, it CAN'T EXIST as a "normal number"

43. awn786

thank u so much.

44. awn786

^^^^^^ @GCR92

45. GCR92

so mathematicians around XVII century had to figure out another type of numbers, called COMPLEX numbers, and the first number of complex numbers is $\sqrt{-1}$

46. GCR92

they INVENTED it

47. GCR92

you are welcome

48. awn786

ur a genius @GCR92

49. GCR92

not really, but thanks!

50. GCR92

ill draw you something

51. awn786

you can bring the most complex thing and make others understand. are u sure ur not related to prfsr. brian cox

52. GCR92

|dw:1358026644045:dw|

53. GCR92

hahaha you amuse me, nothing is hard when you have an amazing teacher, and I have it right now.

54. GCR92

you understand what I drew?

55. awn786

yeah u drew a number line. who is ur teacher

56. GCR92

My uncle, who's been teaching maths since he was 15 and he's now 57, anyway, let's go back to our imagination

57. awn786

|dw:1358026974868:dw|

58. GCR92

ALMOST

59. awn786

|dw:1358027044754:dw|

60. awn786

|dw:1358027175723:dw|

61. GCR92

|dw:1358027034198:dw|

62. GCR92

you put the axis pararell and it's perpendicular cutting in 0

63. awn786

|dw:1358027255837:dw|

64. GCR92

that's why i said almost, because you figured out ANOTHER line, and that would make a 300 year old mathematician proud

65. awn786

yepeee

66. GCR92

because they CAN be negative in their new axis, the imaginary axis

67. GCR92

the imaginary line

68. GCR92

it is not allowed to be a negative square root in the REAL line, but it is in the imaginary one

69. awn786

so in imaginative can they ever be 3i or always do they have to be -3i

70. GCR92

so we just call it i, like we call 1 one

71. GCR92

there are imaginary postive numbers and imaginary negative numbers, under 0

72. GCR92

real negatives are at the left of 0, so why can't there be negative imaginary ones?

73. awn786

|dw:1358027454145:dw|

74. awn786

above 0 is positive?

75. GCR92

if you delete the minus inside of the root, it would be a real number then!

76. GCR92

Yes that's what i was writting

77. GCR92

and under 0 negative, i forgot to draw it

78. GCR92

just like the real line but perpendicular

79. GCR92

above 0 goes posstive until inifinity and under 0 negative until infinity

80. awn786

and on the real line is it same?

81. GCR92

|dw:1358027632303:dw|

82. GCR92

they are two separated lines.

83. awn786

bye i need to go. if i see u tommorw here i will carry on the conversation.

84. GCR92

okay, sure! bye! you are smart btw, you figured the other line very well.

85. GCR92

figured out*

86. awn786

thanks

87. awn786

@GCR92 im back

complex numbers

89. AravindG

i is actually an imaginary number used to give value to $\sqrt{-1}$

90. awn786

yes i get that.

91. awn786

Look above^

92. ParthKohli

Wait, no!

93. awn786

what?

94. ParthKohli

$$i$$ is defined as the imaginary number such that $$i^2 = -1$$, not $$i= \sqrt{-1}$$.

95. awn786

no ur wrong

96. awn786

wait

97. ParthKohli

How so...?

98. awn786

watch

99. awn786

wait

100. awn786
101. awn786

and also its just common knowlige

102. awn786

Knowledge*

103. ParthKohli

Yes, $$i$$ is one of the square roots of $$-1$$. But $$i \ne \sqrt{-1}$$.

104. ParthKohli

I mean, $$\sqrt{-1} =i,-i$$

105. ParthKohli

So you must define $$i^2 = -1$$ if you don't want things to mess up

106. awn786

wow gcr92 was WAY better at explaining things

107. ParthKohli

What would you like to learn?

108. awn786

apparantly his teacher is hgis uncle who started teaching him maths when he was 15 an now is 50

109. awn786

wait

110. awn786

carry on from:

111. awn786

|dw:1358591619083:dw|

112. awn786

look above^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

113. ParthKohli

Re and Co, yes.

114. nikhilchabe

Here you go with the link for complete solution! http://www.learnalberta.ca/content/memg/Division03/Square%20Root/index.html

115. awn786

ermmm it needs to be simple

116. awn786

nope its not

117. awn786

sorry

118. awn786

where is GCR92

119. GCR92

Here. What's up?