Question

If (12x-6)+i(4y+2) =0, then the value of x+y=.​

Answer 1

Answer:

0

Step-by-step explanation:

x+y=6/12+-2/4

=0

I think my answer is correct

Answer 2

If (12x - 6) + i(4y + 2) = 0 then the value of x + y = 0

Given :

(12x - 6) + i(4y + 2) = 0

To find :

The value of x + y

Concept :

Complex Number

A complex number z = a + ib is defined as an ordered pair of Real numbers ( a, b) that satisfies the following conditions :

(i) Condition for equality :

(a, b) = (c, d) if and only if a = c, b = d

(ii) Definition of addition :

(a, b) + (c, d) = (a+c, b+ d)

(iii) Definition of multiplication :

(a, b). (c, d) = (ac-bd , ad+bc )

Of the ordered pair (a, b) the first component a is called Real part of z and the second component b is called Imaginary part of z

Solution :

Step 1 of 3 :

Write down the given equation

Here the given equation is

(12x - 6) + i(4y + 2) = 0

Step 2 of 3 :

Find the value of x and y

$\displaystyle \sf{ (12x - 6) + i(4y + 2) = 0 }$

$\displaystyle \sf{ \implies (12x - 6) + i(4y + 2) = 0 + 0i}$

By the property of equality

12x - 6 = 0 - - - - - - (1)

4y + 2 = 0 - - - - - - (2)

From Equation 1 we get

$\displaystyle \sf{ 12x = 6 }$

$\displaystyle \sf{ \implies x = \frac{6}{12} }$

$\displaystyle \sf{ \implies x = \frac{1}{2} }$

From Equation 2 we get

$\displaystyle \sf{ 4y + 2 = 0 }$

$\displaystyle \sf{ \implies 4y = - 2}$

$\displaystyle \sf{ \implies y = - \frac{2}{4} }$

$\displaystyle \sf{ \implies y = - \frac{1}{2} }$

Step 3 of 3 :

Find the value of x + y

$\displaystyle \sf{ x + y}$

$\displaystyle \sf{ = \frac{1}{2} - \frac{1}{2} }$

$\displaystyle \sf{ = 0 }$

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