Question

Simplify this radical √-4 Does it matter it's a negative? Will it eventually become positive?

Answer 1

\[\large \sqrt{-4} = \sqrt{-1*4}\]

\[\large \sqrt{-4} = \sqrt{-1}*\sqrt{4}\]

\[\large \sqrt{-4} = i*2\]

\[\large \sqrt{-4} = 2i\]

Answer 2

by definition, \[\large i = \sqrt{-1}\]

Answer 3

wow that was super quick. :)

Answer 4

glad to be of help

Answer 5

what is i imaginary number

Answer 6

yes, defined to be the square root of -1

Answer 7

it's not a fair name since all numbers are imaginary really

Answer 8

are you confusing imaginary and complex @jim_thompson5910 ?

Answer 9

no, i is an imaginary number

Answer 10

something like 3+i is a complex number

i is also complex as well

Answer 11

since i = 0+1i

Answer 12

True, so having a negative number does affect the outcome. I read it didn't because both negatives will become positive

Answer 13

\(i\) in not a complex number, \(i\) is a purely imaginary number

Answer 14

not sure what you mean exactly newatthis

Answer 15

i is in the complex number set

Answer 16

i = 0+1i

it's of the form a+bi where a = 0, b = 1

Answer 17

I'm just a bit confused with negative √ simplified radical

Answer 18

i thought to be complex a and b were necessarily non-zero

Answer 19

just keep in mind that x^2 is always positive or 0

so if x^2 = -4 for instance, then there are no real solutions

but if you make the definition that i = sqrt(-1), then you can come up with 2 complex solutions

Answer 20

Nope, as a matter of fact 2 is a complex number also. Complex space enclose both real and imaginary

Answer 21

well yeah if you had the number 3, it's a real number, but it's also part of the complex number system

so 3 is technically complex although we'd just say it's real

Answer 22

yeah akorn103 has the right idea

Answer 23

I think he just misunderstood you when you said that all numbers were imaginary and thought you were making a mathematical and not "philosophical" statement hah

Answer 24

I'm lost but I appreciate the help guys.

Answer 25

just follow the steps I outlined (write them in your notes if that helps) and keep in mind that \[\large i = \sqrt{-1}\]

Answer 26

i is negative -1 so -1 is an imaginary number correct?

Answer 27

i is the square root of -1

Answer 28

Thank you guys your so sweet I appreciate this :)

Answer 29

ok i concede , complex numbers are a superset of real and imaginary numbers

but its like calling a square a rectangle (its true, but misleading )

Answer 30

ehh, it gets more important in linear algebra and beyond