Question

what kind of number is 4+sqrt-25

Answer 1

What happens when you try to evaluate \(\Large \sqrt{-25}\) ?

Answer 2

you get -5i

Answer 3

and therefore complex number

Answer 4

because it is a mixture between imaginary and real number?

Answer 5

good way to put it yes

Answer 6

not -5i, just 5i

Answer 7

\(\Large \sqrt{-25} = 5i\)

\(\Large -\sqrt{-25} = -5i\)

Answer 8

general form for complex number a + bI

Answer 9

oh sorry i accidently put that there. I dont know why i put a -5

Answer 10

a and b are real I = rt of -1

Answer 11

@jim_thompson5910 I think both would be correct
rt-25 = rt-1* rt25 using +ve and neg values for rt 25
-5I and 5I

Answer 12

no, the square root function only produces one output for any given input

I'm using the complex number version of the square root function

Answer 13

are you saying there is a rule when using complex numbers to use one or the other ?

Answer 14

if using a calculator will give the absolute value yes


(-x)^2 = (x)^2

Answer 15

it is true that (5i)^2 = -25 and (-5i)^2 = -25

therefore, x^2 = -25 has the solutions x = 5i or x = -5i

Answer 16

however, the square root function only returns one exact value when you input a number

example: sqrt(9) = 3

it's not sqrt(9) = 3 or -3

Answer 17

if you want the plus or minus, you have to explicitly tack it on \(\Large \pm\sqrt{9} = \pm 3\)