Question

Simplify the number using imaginary unit i.

√-16

^that's square root -16.

PLEASE help! I will give medal to best answer! Show all steps please!

Answer 1

Square root of 16 is easy! 4

Square root of a negative number means you will get "i"

So we will get

4i

Answer 2

That's all the steps to the problem? Wow! I feel dumb for needing to post this, lol. Thank you!!

Answer 3

\(\bf\color{red}{ i = \sqrt{-1}}\qquad thus\\ \quad \\
\sqrt{-16}\implies \sqrt{16}\times \sqrt{-1}\implies \sqrt{4^2}\times \sqrt{-1}\implies 4\times i\implies 4i\)

Answer 4

Its okay! Don't feel dumb, @jdoe0001 has listed a really nice solution for you.

Just split up the "i" portion of the problem and the sqrt portion of the problem and they will be a bit easier!

Answer 5

Could one of you help me with another problem?

Answer 6

Sure! Go ahead and message me your link

Answer 7

Simplify the expression.
-5+i/2i

*that's in fraction form*

Answer 8

@jdoe0001 @jim_thompson5910

Answer 9

@mathstudent55 @mathman806

Answer 10

Hint: multiply top and bottom by 'i'

\[\large \frac{-5+i}{2i}\]

\[\large \frac{(-5+i)*i}{2i*i}\]

I'll let you finish up

Answer 11

\[\frac{-5i^{2}}{2i^2 }\]

Answer 12

Right @jim_thompson5910?

Answer 13

close, the numerator should be \(\large -10i + 2i^2\)

Answer 14

there are more steps after that

hint: \(\large i^2 = -1\)

Answer 15

\[\frac{ 5 }{ 8 }\]

Answer 16

not sure how you got that

Answer 17

i subbed in -1 for all i terms

Answer 18

\(\bf \cfrac{(-5+i)\times i}{2i\times i}\implies \cfrac{-5i+i^2}{2i^2}\)

Answer 19

\(\bf \cfrac{(-5+i)\times i}{2i\times i}\implies\cfrac{(-5\times i)+(i\times i)}{2i^2}\implies
\cfrac{-5i+i^2}{2i^2}\)

Answer 20

\(\bf \textit{recall that}\\ \quad \\
i^2\implies \sqrt{1}\times \sqrt{1}\implies (\sqrt{-1})^2\implies \sqrt{(-1)^2}\implies -1\)

Answer 21

ahemm... well.. rather \(\bf i^2\implies \sqrt{-1}\times \sqrt{-1}\implies (\sqrt{-1})^2\implies \sqrt{(-1)^2}\implies -1\)