Answer:
[tex]3i+3[/tex]
Step-by-step explanation:
The given expression is [tex]\frac{6i}{1+i}[/tex]
Rationalize the denominator:
Multiply numerator and denominator by the conjugate of the denominator.
Hence, multiply numerator and denominator by 1-i
[tex]\frac{6i}{1-i}\cdot\frac{1+i}{1-i}[/tex]
Multiply the denominator using the formula [tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]\frac{6i(1-i)}{1^2-i^2}[/tex]
Now, i^2 = -1
[tex]\frac{6i(1-i)}{1-(-1)}\\\\\=\frac{6i(1-i)}{2}\\\\=3i(1-i)\\\\=3i+3i^2\\\\3i-3(-1)\\\\3i+3[/tex]
Therefore, the value of the given expression is [tex]3i+3[/tex]
