## JenniferSmart1 2 years ago why is this true? $\frac{2}{8i}=-\frac i 4$

1. satellite73

first off you can reduce, just like with real numbers then multiply top and bottom by $$i$$

2. matricked

because i*i=-1

3. matricked

or 1/i=-i

4. JenniferSmart1

Is our goal to get the imaginary number out of the denominator?

5. sauravshakya

|dw:1358398893659:dw|

6. satellite73

$\frac{2}{8i}=\frac{1}{4i}=\frac{1}{4i}\times \frac{i}{i}=\frac{i}{4i^2}=-\frac{i}{4}$

7. sauravshakya

What is wrong if I say 1/i=i

8. satellite73

it is $$\frac{1}{i}=-i$$

9. satellite73

@sauravshakya you cannot use $$\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$$ unless $$a$$ and $$b$$ are real

10. sauravshakya

ya I got how u got 1/i=-i But |dw:1358399037098:dw| this doesn't work

11. satellite73

no it does not

12. sauravshakya

1 and -1 are real

13. satellite73

even this doesn't work $\sqrt{a}\sqrt{b}=\sqrt{ab}$ unless $$a$$ and $$b$$ are positive numbers

14. satellite73

excuse me i said 'real' and i meant 'positive' my mistake

15. sauravshakya

oh I got it...

16. satellite73

@JenniferSmart1 yes the goal is to get the complex number out of the denominator to write in standard form $$a+bi$$

17. JenniferSmart1

oh ok

18. JenniferSmart1

make sense

19. JenniferSmart1

so i*i=-1?

20. JenniferSmart1

I'm too tired...I'll look at it again tomorrow. Thanks guys