# fasilities

• Jun 9th 2010, 06:45 AM
dapore
fasilities
• Jun 9th 2010, 07:09 AM
sa-ri-ga-ma
Quote:

What do you mean by facilities?
• Jun 9th 2010, 07:29 AM
Soroban
Hello, dapore!

What does "facilities" mean?

If it means "equals", there is no solution.

Quote:

$\displaystyle \text{If }\;\frac{3-2i}{i}\;\text{ facilities }\:\frac{x-5y}{1+5i},\;\text{ find }x,y$

Rationalize the left side:

. . $\displaystyle \frac{3-2i}{i}\cdot\frac{-i}{-i} \:=\:-2-3i$ .[1]

Rationalize the right side:

. . $\displaystyle \frac{x-5y}{1+5i}\cdot\frac{1-5i}{1-5i} \;=\; \frac{(x-5y) - 5(x-5y)i}{26}$ .[2]

Equate [1] and [2]: .$\displaystyle -2-3i \;=\;\frac{(x-5y) - 5(x-5y)i}{26}$

. . $\displaystyle -52 - 78i \;=\;(x-5y) - 5(x-5y)i$

Equate real and imaginary components:

. . $\displaystyle \begin{array}{ccc}x - 5y &=& -52 \\ -5(x-5y) &=& -78 \end{array}$

The system: .$\displaystyle \begin{Bmatrix}x-5y &-& -52 \\ x-5y &=& \frac{78}{5}\end{Bmatrix}$ .is inconsistent.

• Jun 9th 2010, 07:33 AM
dapore
Quote:

Originally Posted by sa-ri-ga-ma
What do you mean by facilities?

x+yi is fasilities for x-yi