Question

please help me with this​

Answer 1

Answer:

3+2i

Step-by-step explanation:

see attachment for explanation

Answer 2

. A useful property is that the product of any number with its complex conjugate is a real number. We will use that to eliminate the complex number from the denominator.

To find a complex conjugate, simply change the sign of the imaginary part (the part with the i ). This means that it either goes from positive to negative or from negative to positive. As a general rule, the complex conjugate of a+bi is a−bi . Therefore, the complex conjugate of 3−2i is 3+2i .

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

25

63−16i

Step-by-step explanation:

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

(1+2i)(2−i)

(3−2i)(2+3i)

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}

(1+2i)(2−i)

(3−2i)(2+3i)

=

2−i+4i−2i

2

6+9i−4i−6i

2

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

(1+2i)(2−i)

(3−2i)(2+3i)

=

2+3i+2

6+5i+6

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

(1+2i)(2−i)

(3−2i)(2+3i)

=

4+3i

12+5i

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

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

4+3i

12+5i

×

4−3i

4−3i

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

16−9i

2

48−36i+20i−15i

2

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

16+9

48+15−16i

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

25

63−16i

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

25

63−16i

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