Question

if (a+b)(2+i) = b + 1 + (10+2a)i then a and b are​

Answer 1

ANSWER:

Given:

• (a+b)(2+i) = b + 1 + (10+2a)i

To Find:

• Value of a and b

Solution:

We are given that,

⇒(a+b)(2+i) = b + 1 + (10+2a)i

⇒2(a + b) + (a + b)i = b + 1 + (10 + 2a)i

Now, we will compare the real and imaginary parts. So,

REAL PART:

⇒2(a + b) = b + 1

⇒2a + 2b = b + 1

⇒2a + 2b - b = 1

⇒2a + b = 1 --------(1)

IMAGINARY PART:

⇒a + b = 10 + 2a

⇒10 + 2a = a + b

⇒10 + 2a - a - b = 0

⇒a - b = -10 --------(2)

Now, we will add (1) & (2),

⇒2a + b + a - b = 1 - 10

⇒3a = -9

⇒a = -9/3

⇒a = -3

Putting value of a in (2),

⇒a - b = -10

⇒-3 - b = -10

⇒3 + b = 10

⇒b = 10 - 3

⇒b = 7

Hence, a = -3 and b = 7.

Answer 2

Step-by-step explanation:

ANSWER:

Given:

(a+b)(2+i) = b + 1 + (10+2a)i

To Find:

Value of a and b

Solution:

We are given that,

⇒(a+b)(2+i) = b + 1 + (10+2a)i

⇒2(a + b) + (a + b)i = b + 1 + (10 + 2a)i

Now, we will compare the real and imaginary parts. So,

REAL PART:

⇒2(a + b) = b + 1

⇒2a + 2b = b + 1

⇒2a + 2b - b = 1

⇒2a + b = 1 --------(1)

IMAGINARY PART:

⇒a + b = 10 + 2a

⇒10 + 2a = a + b

⇒10 + 2a - a - b = 0

⇒a - b = -10 --------(2)

Now, we will add (1) & (2),

⇒2a + b + a - b = 1 - 10

⇒3a = -9

⇒a = -9/3

⇒a = -3

Putting value of a in (2),

⇒a - b = -10

⇒-3 - b = -10

⇒3 + b = 10

⇒b = 10 - 3

⇒b = 7

Hence, a = -3 and b = 7.