fasilities

**sa-ri-ga-ma** · June 9th 2010, 07:09 AM

Originally Posted by dapore

What do you mean by facilities?

**Soroban** · June 9th 2010, 07:29 AM

Hello, dapore!

What does "facilities" mean?

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

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

Rationalize the left side:

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

Rationalize the right side:

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

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

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

Equate real and imaginary components:

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

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

**dapore** · June 9th 2010, 07:33 AM

Originally Posted by sa-ri-ga-ma

What do you mean by facilities?

x+yi is fasilities for x-yi

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