Question

(Complex Numbers) Multiply or divide as indicated: √-7 * √-15

Answer 1

\(\bf \sqrt{-7}\cdot \sqrt{-15}\implies \sqrt{-7\cdot -15}\implies \quad ?\)

Answer 2

@jdoe0001 you can't multiply complex numbers that way, you first have to pull out the i
\[\large \sqrt{-7}\cdot \sqrt{-15} = i \sqrt 7 *i \sqrt 15\]
\[\Large i*i \sqrt 7 \sqrt {15} =\]
\[\Large i^2 \sqrt {7*15}\]

Answer 3

In the answer key, it ends up being: -√105 so does the i^2 become the negative that is before the square root symbol?

Answer 4

yeah
\[ i=\sqrt{-1}\]
\[i^2 = -1\]

Answer 5

How is it a negative though whenever: -1*-1=1

Answer 6

since
\[\sqrt{-1}≠-1 \quad ; \quad \sqrt{-1} = i\]
so
\[ i^2 = i*i=\sqrt{-1}\sqrt{-1}=(-1)^{1/2}\cdot (-1)^{1/2} =(-1)^1 = -1\]

Answer 7

hmm... ohhh

Answer 8

\(\bf i^2\implies \sqrt{-1}\cdot \sqrt{-1}\implies (\sqrt{-1})^2\implies \sqrt{(-1)^2}\implies -1\)

Answer 9

\(\bf \sqrt{-7}\cdot \sqrt{-15}\implies \sqrt{7}\ i\cdot \sqrt{15}\ i\implies \sqrt{105}\ i^2\implies -\sqrt{105}\)

Answer 10

does that make sense @DemiRae ?

Answer 11

Yeah that makes sense, I wasn't thinking of them in their square root form. Thank you for helping me with that!