Question

help please need quick repsone

Answer 1

\[\sqrt -36 \over 2+5i\]

Answer 2

rationalize the denominator

Answer 3

@phi @iGreen @Mashy @caitlinnr14 @ganeshie8

Answer 4

@amistre64

Answer 5

please show steps

Answer 6

what does it mean to rationalize something?

Answer 7

one sec let me think

Answer 8

getting all the 'radical' signs out of it

Answer 9

thats part of it sure. but in general, we want to convert something into a rational number.

we have a complex number on the bottom that they want converted to a rational real number

Answer 10

oh

Answer 11

complex numbers are converted using a conjugate since:

(a^2 - b^2) = (a+b)(a-b)

Answer 12

when b is a pure imaginary value like say 3i

a^2 - (3i)^2 = a^2 -9i^2

but i^2 = -1

a^2 -9(-1) = a^2 + 9

Answer 13

is looks like the same principle from my last question

Answer 14

ok im starting to understand it

Answer 15

so, this gives us a similar formula:

a^2 + b^2 = (a + bi) (a - bi)

Answer 16

so using a conjugate we end up with

sqrt(-36) 2-5i
-------- * -----
2+5i 2-5i

Answer 17

so basicly you multiply out the complex terms conjate factors in the denominator to remove the imagery terms

Answer 18

yep

Answer 19

ok so that would be the answer

Answer 20

show me what your solution looks like

Answer 21

simplified or

Answer 22

simplified is fine ... ill know if you messed up :)

Answer 23

simplified it would be 30/29 + 12i / 29

Answer 24

29 is good

now the top, lets chk

sqrt(-36) = sqrt(36) sqrt(-1) = 6i

6i(2 - 5i) = 12i -30i^2 = 12i -30(-1)


30+12i
-------
29

:):)

Answer 25

yours is good

Answer 26

thx

Answer 27

yw :)