Question

If 4x + (3x – y)i = 3 – 6i , then values of x and y.

(a)x=3/4, y=33/4, (b) x=33/4, y=3/4 (c) x=-33/4, y=3 (d) x=-2, y=3​

Answer 1

If 4x + (3x – y)i = 3 – 6i , then values of x and y.

The correct answer is x = 3/4 and y  = 33/4 option(a)

Step-by-step explanation:

Given, 4x + (3x – y)i = 3 – 6i

By equating the real and imaginary parts,

(I) 4x = 3

     x = 3/4

(ii) 3x - y = - 6

Substituting the 'x' value here,

 3(3/4) - y = -6

 9/4 - y = - 6

 9/4 + 6 = y

  y   = 9/4 + 6

      = 9 +6(4) / 4

      = 9 + 24/ 4

  y  = 33/4

Therefore, the value of x and y from the given problem is 3/4 and 33/4 respectively.

Answer 2

SOLUTION

GIVEN

4x + (3x – y)i = 3 – 6i ,

TO CHOOSE THE CORRECT OPTION

The values of x and y

(a) x = 3/4, y = 33/4

(b) x = 33/4, y = 3/4

(c) x = - 33/4, y = 3

(d) x = - 2 , y = 3

CONCEPT TO BE IMPLEMENTED

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

EVALUATION

Here it is given that

4x + (3x – y)i = 3 – 6i

By the property of equality

4x = 3 ......... (1)

And

3x - y = - 6 ........ (2)

From Equation (1) we get

$\displaystyle \sf{x = \frac{3}{4} }$

Putting the value of x in Equation (2) we get

$\displaystyle \sf{ \bigg(3 \times \frac{3}{4} \bigg)- y = - 6 }$

$\implies \displaystyle \sf{ \frac{9}{4} - y = - 6 }$

$\implies \displaystyle \sf{ y = \frac{9}{4} + 6 }$

$\implies \displaystyle \sf{ y = \frac{9 + 24}{4} }$

$\implies \displaystyle \sf{ y = \frac{33}{4} }$

FINAL ANSWER

The correct option is

$(a) \: \: \: \displaystyle \sf{x = \frac{3}{4} \: \: , \: \: y = \frac{33}{4} }$

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