Question

abi=3a-b+12i , find a & b​

Answer 1

Answer:

The value is a = 2 and b = 6 or a = -2 and b = -6.

Step-by-step explanation:

Consider the provided information.

$abi=3a-b+12i$

The above equation has two parts i.e. imaginary and real.

The part which is multiple of "i " is know as imaginary part otherwise it is know as the real part.

In the above equation ab and 12 is the multiple of "i " therefore, they are imaginary part whereas 3a and b is not the multiple of "i " so, they are real part.

The provided equation can be written as:

$0+abi=3a-b+12i$

Now, we will compare the real part with real and imaginary part with imaginary as shown below:

$0=3a-b$ and $ab=12$

Consider the equation $0=3a-b$.

$0=3a-b$

$b=3a$

Substitute the value of b in $ab=12$

$a(3a)=12$

$3a^2=12$

$a^2=4$

$a=\pm 2$

Substitute a = 2 in $b=3a$

$b=3(2)$

$b=6$

Substitute a = -2 in $b=3a$

$b=3(-2)$

$b=-6$

Hence, the value is a = 2 and b = 6 or a = -2 and b = -6.