Simplify .
Answers
Answer:
( 1 + 9i)/4
Step-by-step explanation:
Hi,
Consider 1/1-2i
Multiplying and dividing by 1 + 2i, we get
(1 + 2i)/((1 + 2i)(1 - 2i)
= (1 + 2i)/5-------------------------------------------(1)
Consider 3/1 + i
Multiplying and dividing by 1 - i, we get
3(1 - i)/(1 + i)*(1 - i)
= 3(1 - i)/2
= 3/2 -3i/2------------------------------------------(2)
Consider 1/1-2i + 3/1 + i
From (1) and (2), we get
= (1 + 2i)/5 + 3/2 -3i/2
= (1/5 + 3/2) + i(2/5 - 3/2)
= 17/10 + i(-11/10)
= 17/10 - 11i/10--------------------------------------(3)
Consider (3 + 4i)/(2 - 4i)
Multiplying and dividing by 2 + 4i, we get
[(3 + 4i)*(2 + 4i)/(2 - 4i)*2 + 4i]
= ( 6 - 16 + 12i + 8i)/(4 + 16)
= ( -10 + 20i)/20
= (-1 + 2i)/2---------------------------------------------(4)
Consider [1/1-2i + 3/1 + i]*[(3 + 4i)/(2 - 4i)]
From (3) and (4), we get
(17/10 - 11i/10)*( (-1 + 2i)/2)
= (17 - 11i)*(-1 + 2i)/20
= ( -17 + 22 + 34i + 11i)/20
= (5 + 45i)/20
= ( 1 + 9i)/4
Hope, it helps !