Question

Evaluate (6 + 2i) / (3 –i ).
5/4 + 6/4i
8/5 + 6/5i
20/8 + 12/8i
16/9 + 12/9i

Answer 1

Answer: 8/5+6/4i

Proof of validity is shown below.

Answer 2

We are given with a complex no. and need to simplify it , so let's start !!!

Let's assume that :

`{:\implies \quad z=\sf (6+2\iota)/(3-\iota)}`

Now , Rationalizing the denominator or in other words multiplying and dividing
`{z}` by the conjugate of the denominator

`{:\implies \quad z=\sf (6+2\iota)/(3-\iota)* (3+\iota)/(3+\iota)}`

`{:\implies \quad z=\sf ((6+2\iota)(3+\iota))/((3-\iota)(3+\iota))}`

`{:\implies \quad z=\sf (6(3+\iota)+2\iota (3+\iota))/((3)^(2)-(\iota)^(2))\quad \qquad \{\because (a-b)(a+b)=a^(2)-b^(2)\}}`

`{:\implies \quad z=\sf (18+6\iota +6\iota +2(\iota)^(2))/(9-(-1))\quad \qquad \{\because (\iota)^(2)=-1\}}`

`{:\implies \quad z=\sf (18+12\iota -2)/(10)}`

`{:\implies \quad z=\sf (16+12\iota)/(10)}`

`{:\implies \quad z=\sf (16)/(10)+(12\iota)/(10)}`

`{:\implies \quad {\bf \therefore}\quad \underline{\underline{z=\bf (8)/(5)+(6)/(5)\iota}}}`

Hence , Option B) (8/5) + (6/5)i is correct :D