Question

Express the following in the form of a+ib, a, b€R i=√-1. state the value of a and b​

Answer 1

Answer:

a = -7/2

b = 1/2

Step-by-step explanation:

We are given that

i(4 + 3i) / (1 - i)

By rationalization that is multiplying and dividing by 1 + i  we get

= i(4 + 3i)(1 + i) / (1 - i)(1 + i)

= (4i + 3i²)(1 + i) / (1² - i²)            

= (4i - 3)(1 + i) / (1² - i²)            ∵ i² = -1

= (4i + 4i² - 3 - 3i) / (1 + 1)        ∵ i² = -1

= (i - 4 - 3) / 2

= (i - 7) / 2

= -7/2 + i/2

= -7/2 + (1/2)i

By comparing with

a + bi

we get

a = -7/2

b = 1/2