Question

Q2. Find the real value of the x and y if (3x – 7) + 2iy = –5y + (5 + x) i​

Answer 1

Answer:

• In this case we have 3x - 7 = -5y and 2y = 5 + x. These are better written as 3x + 5y = 7 and x - 2y = -5. The second of these becomes 3x - 6y = -15, and so subtracting the 2 equations gives 11y = 22, and so y = 2.

Step-by-step explanation:

• please make it a brainliest answer.

Answer 2

$\large\underline{\sf{Solution-}}$

We know that,

Two complex numbers

$\red{\rm :\longmapsto\:z_1 = a + ib}$

and

$\red{\rm :\longmapsto\:z_2 = c + id}$

are equal iff

$\red{\boxed{ \bf{ \: Re(z_1) = Re(z_2), \: \: i.e \: a = c}}}$

and

$\red{\boxed{ \bf{ \: Im(z_1) = Im(z_2), \: \: i.e \: b = d}}}$

So, it is given that

$\rm :\longmapsto\:(3x – 7) + 2iy = –5y + (5 + x) i$

So, on comparing, we get

$\rm :\longmapsto\:3x - 7 = - 5y$

can be rewritten as

$\rm :\longmapsto\:3x + 5y = 7 - - - (1)$

Also,

$\rm :\longmapsto\:5 + x = 2y$

$\rm :\longmapsto\: x = 2y - 5 - - - - (2)$

On substituting the value of x, in equation (2), we get

$\rm :\longmapsto\:3(2y - 5) + 5y = 7$

$\rm :\longmapsto\:6y - 15+ 5y = 7$

$\rm :\longmapsto\:11y = 7 + 15$

$\rm :\longmapsto\:11y = 22$

$\bf\implies \:y = 2$

On substituting y = 2, in equation (2), we get

$\rm :\longmapsto\:x = 2 \times 2 - 5$

$\rm :\longmapsto\:x = 4 - 5$

$\bf\implies \:x = - \: 1$

Additional Information :-

$\boxed{ \bf{ \: {i}^{2} = - 1}}$

$\boxed{ \bf{ \: {i}^{3} = - i}}$

$\boxed{ \bf{ \: {i}^{4} = 1}}$

$\boxed{ \bf{ \: \frac{1}{i} = - \: i}}$