Question

What is the value of 6i/1+i

Answer 1

its d: 3+3i

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Answer 2

`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`