## anonymous 3 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. anonymous

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

2. anonymous

3. anonymous

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. anonymous

so what is an imaginary unit

5. anonymous

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

6. anonymous

yes what is the vid @zaynahf

7. hba

did you see the link @awn786 It has everything.

8. anonymous

yes i did but what is an imaganary unit

9. anonymous
10. anonymous

WOW OMG complicated @hba

11. anonymous

The first link is really straight forward, try that

12. hba

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

13. anonymous

thanks for trying. @hba

14. hba

You are welcome :)

15. anonymous

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

16. anonymous

17. anonymous

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. anonymous

whats w

20. hba

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

21. anonymous

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. anonymous

whats omega

25. hba

26. anonymous

27. hba

Well,In numbers it is sqrt{-1}

28. anonymous

it should be easy shouldent it.

29. anonymous

30. anonymous

what is omega

31. hba

I have already told you what omega is.

32. anonymous

no u havent @hba

33. hba

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

34. anonymous

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

35. anonymous

$\sqrt{-1}$ 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. anonymous

you just need to know what a square root is

37. anonymous

i know what a square root is ofc

38. anonymous

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

39. anonymous

(possitive)

40. anonymous

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

41. anonymous

you have the best responce

42. anonymous

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

43. anonymous

thank u so much.

44. anonymous

^^^^^^ @GCR92

45. anonymous

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. anonymous

they INVENTED it

47. anonymous

you are welcome

48. anonymous

ur a genius @GCR92

49. anonymous

not really, but thanks!

50. anonymous

ill draw you something

51. anonymous

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

52. anonymous

|dw:1358026644045:dw|

53. anonymous

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

54. anonymous

you understand what I drew?

55. anonymous

yeah u drew a number line. who is ur teacher

56. anonymous

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. anonymous

|dw:1358026974868:dw|

58. anonymous

ALMOST

59. anonymous

|dw:1358027044754:dw|

60. anonymous

|dw:1358027175723:dw|

61. anonymous

|dw:1358027034198:dw|

62. anonymous

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

63. anonymous

|dw:1358027255837:dw|

64. anonymous

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

65. anonymous

yepeee

66. anonymous

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

67. anonymous

the imaginary line

68. anonymous

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

69. anonymous

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

70. anonymous

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

71. anonymous

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

72. anonymous

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

73. anonymous

|dw:1358027454145:dw|

74. anonymous

above 0 is positive?

75. anonymous

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

76. anonymous

Yes that's what i was writting

77. anonymous

and under 0 negative, i forgot to draw it

78. anonymous

just like the real line but perpendicular

79. anonymous

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

80. anonymous

and on the real line is it same?

81. anonymous

|dw:1358027632303:dw|

82. anonymous

they are two separated lines.

83. anonymous

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

84. anonymous

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

85. anonymous

figured out*

86. anonymous

thanks

87. anonymous

@GCR92 im back

88. anonymous

complex numbers

89. AravindG

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

90. anonymous

yes i get that.

91. anonymous

Look above^

92. ParthKohli

Wait, no!

93. anonymous

what?

94. ParthKohli

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

95. anonymous

no ur wrong

96. anonymous

wait

97. ParthKohli

How so...?

98. anonymous

watch

99. anonymous

wait

100. anonymous
101. anonymous

and also its just common knowlige

102. anonymous

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. anonymous

wow gcr92 was WAY better at explaining things

107. ParthKohli

What would you like to learn?

108. anonymous

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

109. anonymous

wait

110. anonymous

carry on from:

111. anonymous

|dw:1358591619083:dw|

112. anonymous

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

113. ParthKohli

Re and Co, yes.

114. anonymous

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

115. anonymous

ermmm it needs to be simple

116. anonymous

nope its not

117. anonymous

sorry

118. anonymous

where is GCR92

119. anonymous

Here. What's up?