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

User Nevir
by
6.6k points

2 Answers

9 votes

Answer: 8/5+6/4i

Proof of validity is shown below.

Evaluate (6 + 2i) / (3 –i ). 5/4 + 6/4i 8/5 + 6/5i 20/8 + 12/8i 16/9 + 12/9i-example-1
User Jerfeson Guerreiro
by
7.3k points
5 votes

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

User JonnySerra
by
6.8k points