Question

Find the conjugate of (3-2i)(2+3i)/(1+2i)(2-i)

Answer 1

Hope this will help you.

Answer 2

Answer:

The conjugate form of the expression is $\frac{63-16i}{25}$

Step-by-step explanation:

Given : Expression $\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}$

To find : The conjugate of the expression?

Solution :

Conjugate means rationalize the given denominator with opposite sign of imaginary term.

First we solve the expression,

$\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}=\frac{6+9i-4i-6i^2}{2-i+4i-2i^2}$

$\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}=\frac{6+5i+6}{2+3i+2}$

$\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}=\frac{12+5i}{4+3i}$

Now, we rationalize the denominator by 4-3i.

$=\frac{12+5i}{4+3i}\times \frac{4-3i}{4-3i}$

$=\frac{48-36i+20i-15i^2}{16-9i^2}$

$=\frac{48+15-16i}{16+9}$

$=\frac{63-16i}{25}$

Therefore, The conjugate form of the expression is $\frac{63-16i}{25}$