Question

Find the values of x and y that satisfies the equation. 5x + 3i = 15 + yi

Answer 1

Answer:  The required value of x is 3 and that of y is 3.

Step-by-step explanation:  We are given to find the values of x and y that satisfies the following equation :

$5x+3i=15+yi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

$a+bi=c+di~~~~~~~~~\Rightarrow a=c,~b=d.$

That is, the real and parts on both sides of the equation are equal.

From equation (i), we have

$5x+3i=15+yi.$

Equating the real and imaginary parts on both sides of the above equation, we get

$5x=15\\\\\Rightarrow x=\dfrac{15}{5}\\\\\Rightarrow x=3$

and

$3=y\\\\\Rightarrow y=3.$

Thus, the required value of x is 3 and that of y is 3.

Answer 2

Answer:

So the value of x=3  and y =3

Step-by-step explanation:

5x + 3i = 15 + yi

To find out x   , set the constant terms  equal to each other and solve for x

5x= 15

Divide by 5 on both sides

x= 3

To find out y   , set the ';i' terms  equal to each other and solve for y

3= y

So the value of x=3  and y =3