Question

If (1+2i) (1+3i) (2+i) then a+ib form is​

Answer 1

Given :-

( 1 + 2i ) ( 1 + 3i ) ( 2 + i ) .

To Find :-

The given in the form of a + ib .

Used Concepts :-

• Value of iota i.e √-1 and that of i² i.e -1 .

Solution :-

Here , ( 1 + 2i ) ( 1 + 3i ) ( 2 + i )

At first , we will multiply two factors then the third with the product of two factors .

[ ( 1 + 2i ) × ( 1 + 3i ) ] × ( 2 + i )

=> [ 1 × ( 1 + 3i ) + 2i × ( 1 + 3i ) ] × ( 2 + i )

=> [ 1 + 3i + 2i + 6i² ] × ( 2 + i )

=> [ 1 + 5i + 6 × -1 ] × ( 2 + i )

=> [ 1 + 5i - 6 ] × ( 2 + i )

=> ( 2 + i ) × ( 5i - 5 )

=> 2 × ( 5i - 5 ) + i × ( 5i - 5 )

=> 10i - 10 + 5i² - 5i

=> 5i - 10 + 5 × -1

=> 5i - 10 - 5

=> -15 + 5i = -15 + i5

Hence , it is in the form of a + ib , where a = -15 and b = 5 .