Question

(a+b)(2+i)= b+1+ (10+2a) i.
Find value of a and b.​

Answer 1

Answer:

a=-3 and b = 7

Step-by-step explanation:

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

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

Equating the real and imaginary parts

2a + 2b = b+1..... (1)

a+b= 10+2a.....(2)

From 1

2b-b = 1-2a

b = 1-2a.....(3)

From 2

b = 10+2a-a

b = 10+a.....(4)

from 3 and 4

1-2a = 10+a

1-10= a+2a

3a = -9

a= -3

Substituting a = -3 in eq.3

b = 10+a

b = 10-3

b  = 7

hope it helps

Answer 2

Answer:

a=-3 and b=7

Step-by-step explanation:

• (2a+2b)+(ai+bi)=b+1+(10+2a)i
• ai+bi=(10+2a)i
• a+b=10+2a
• b=10+2a-a
• b=10+a
• therefor 2a+2b=b+1
• 2a+2b=b+1
• 2a+2(10+a)=10+a+1
• 2a+20+2a=11+a
• 4a-a =11-20
• 3a=-9
• a=-3
• hence, b=10+a
• b=10+(-3)
• b=10-3
• b=7