Question

Express in the fo of x+iy
​

Answer 1

Step-by-step explanation:

Given :-

(3+√-4)/(4-√-1)

To find :-

Express the given expression in the form of x+iy.

Solution :-

Given that

(3+√-4)/(4-√-1)

We know that i² = -1 => √-1 = i

Now

=> (3+√4i²)/(4-√i²)

=> (3+2i)/(4-i)

On multiplying both numerator and denominator with (4+i) then

=> [(3+2i)/(4-i)]×[(4+i)/(4+i)]

=> [(3+2i)(4+i)]×[(4-i)(4+i)]

=> [3(4+i)+2i(4+i)]/(4²-i²)

Since (a+b)(a-b) = a²-b²

=> (12+3i+8i+2i²)/(16-i²)

=> (12+11i+2(-1))/(16-(-1))

=> (12+11i-2)/(16+1)

=> (10+11i)/17

On writing it in the form of x+iy then

=> (10/17) + (11i/17)

=> (10/17)+(11/17)i

Answer:-

The required answer for the given problem is (10/17)+(11/17)i

Used formulae:-

→ (a+b)(a-b) = a²-b²

→ i² = -1

→ i = √-1