Question

Write the quotient in the form a + bi5/6+2i​plz answer only if you got an answer

Answer 1

Given:

$\dfrac{5}{6+2i}$

To find:

The  quotient in the form a + bi.

Solution:

We have,

$\dfrac{5}{6+2i}$

Multiply numerator and denominator by 6-2i.

$=\dfrac{5\times (6-2i)}{(6+2i)\times (6-2i)}$

$=\dfrac{5(6)+5(-2i)}{6^2+(2i)^2}$

$=\dfrac{30-10i}{36+4i^2}$

$=\dfrac{30-10i}{36+4(-1)}$    $[\because i^2=-1]$

On further simplification, we get

$=\dfrac{30-10i}{36-4}$

$=\dfrac{30-10i}{32}$

$=\dfrac{30}{32}-\dfrac{10i}{32}$

$=\dfrac{15}{16}+(-\dfrac{5}{16})i$

Therefore, the form a+bi is $\dfrac{15}{16}+(-\dfrac{5}{16})i$, where, $a=\dfrac{15}{16}$ and $b=(-\dfrac{5}{16})$.