What is the value of 6i/1+i

Question

asked Aug 7, 2018 226k views

2 Answers

Manu Chadha · Answer 1 · 2018-08-12T02:08:23+0000

Answer:

3i+3

Explanation:

The given expression is
(6i)/(1+i)

Rationalize the denominator:

Multiply numerator and denominator by the conjugate of the denominator.

Hence, multiply numerator and denominator by 1-i

$(6i)/(1-i)\cdot(1+i)/(1-i)$

Multiply the denominator using the formula
(a+b)(a-b)=a^2-b^2

(6i(1-i))/(1^2-i^2)

Now, i^2 = -1

$(6i(1-i))/(1-(-1))\\\\\=(6i(1-i))/(2)\\\\=3i(1-i)\\\\=3i+3i^2\\\\3i-3(-1)\\\\3i+3$

Therefore, the value of the given expression is
3i+3