Question

if a(1-3i)+b(1-2i)=5+2i then a-b=

Answer 1

Answer:

The value of a - b = -29

Step-by-step explanation:

It is given that,

a(1-3i) +b(1-2i) = 5+2i

=> a×1 - a×3i + b×1 - b×2i = 5 +2i

=> a - 3ai +b - 2bi = 5+2i

=> (a+b) + i(-3a - 2b) = 5+2i

By comparing both sides of the equation, we get,

a+b = 5 ----(1) and -3a -2b = 2 ----(2)

So we get two equation (1) and (2),

Now, 2 × (1) + 1×(2),

We get,

2×(a+b) +1×(-3a-2b) = 2×5 +1×2

=> 2a+2b-3a-2b= 10+2

=> -1a= 12

=> a = -12

Therefore the value of a is = -12

And, a+b= 5

Putting value of a, we get,

-12+b= 5

=> b= 5+12= 17

Therefore the value of b is = 17

Now we have to find the value of a-b

So, a-b= -12-17= -29

Therefore the value of a- b = -29

Answer 2

Given:

a(1-3i)+b(1-2i)=5+2i

To Find:

a-b=

Solution:

A complex number is a number that is the square root of a negative one and we do not further try to get the value of it, but instead treat it as a single new variable which is denoted by iota 'i'.

In the given equation we can see that we can find the value of a and b by comparing the real number value and the complex number value individually,

Now simplifying the equation, we have,

a(1-3i)+b(1-2i)=5+2i

a-3ai+b-2bi=5+2i

(a+b)-(3a+2b)i=5+2i

Now comparing both the value we will get equation as,

a+b=5     -(1)

3a+2b=-2     -(2)

Now multiplying the equation 1 with 3 and subtracting with equation2, we have

3a+3b-3a-2b=15+2

b=17

a=-12

so the value of a-b is,

=a-b

=-12-17

=-29

Hence, the value of a-b is -29.