Posted by **Nayla** on Monday, November 23, 2009 at 10:35am.

Does (-7/4i-1) symplify to be -7(1+4i)/18

- Math -
**drwls**, Monday, November 23, 2009 at 11:43am
Not quite. Your parenthese seem to be in the wrong place, and your math is wrong.

-7/(4i-1)= -7(4i+1)/[(4i+1)(4i-1)]

= -7(4i +1)/(-17)

= (7/17)(1+4i)

- Math -
**Nayla**, Monday, November 23, 2009 at 11:45am
These are complex numbers by the way.

- Math -
**Nayla**, Monday, November 23, 2009 at 11:45am
Thanks

- Math -
**Nayla**, Monday, November 23, 2009 at 11:54am
why is the 1+4i on the side of the fraction and not on the top with the 7

- Math -
**MathMate**, Monday, November 23, 2009 at 1:11pm
(7/17)(1+4i) is the same as 7(1+4i)/17.

I too think it is simpler to write it as DRWS did, where the numeric fraction precedes the algebraic part.

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**Jaison**, Monday, November 23, 2009 at 1:18pm
is (7/17)-(28/17i) the same thing

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**MathMate**, Monday, November 23, 2009 at 2:42pm
"is (7/17)-(28/17i) the same thing "

No it is not.

(7/17)*(1+4i)

=(7/17)*1 + (7/17)*4i

=(7/17) + 28i/17

But this is not a simplified version.

In any case the object is to remove the "i" from denominator, or "rationalizing the denominator". Some teachers may consider it incomplete if square-root signs or "i" appear in the denominator.

The reason that the numerator and denominator were multiplied by (1+4i) was to create the product (1+4i)*(1-4i)=-17 in the denominator, thereby rationalizing it.

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