Question

Type the correct answer in the box. Fill in the missing term in the equation.

(1 + 2i)(2 + i) +______= 5(2 + i)

Answer 1

Answer:

The missing term is :  10 .

Step-by-step explanation:

The equation :

( 1 + 2 i ) ( 2 + i ) + x = 5 ( 2 + i )

2 + i + 4 i + 2 i² + x = 10 + 5 i

and because i² = - 1 :

2 + 5 i - 2 + x = 10 + 5 i

x = 10 - 2 + 2 + 5 i - 5 i

x = 10

Answer 2

Answer:

10

Step-by-step explanation:

According to the question,

We need to find the missing term in the equation $(1 + 2i)(2 + i) + -- = 5(2 + i)$,

let the missing term be x

As we know,

i² = - 1

Then,

The equation : $( 1 + 2 i ) ( 2 + i ) + x = 5 ( 2 + i )$

Now,

$( 1 + 2 i ) ( 2 + i ) + x = 5 ( 2 + i )\\\\2 + i + 4 i + 2 i^2 + x = 10 + 5 i~~~~~~~~~~~[because~ i^2 = - 1 ]\\\\2 + 5 i - 2 + x = 10 + 5 i\\\\x = 10 - 2 + 2 + 5 i - 5 i\\\\x = 10$

Hence, the missing term in the equation is 10.