Respuesta :

bcalle
b/a = (3 - 2i)/(2 + i)
To divide complex numbers, you multiply the numerator and denominator by the complex conjugate of the denominator.
The complex conjugate is 2 - i. ** Remember i^2 = -1    **a + bi

( 3 - 2i) ( 2 - i)
-------------------         Foil numerator and denominator.
(2 + i)  ( 2 - i)

 6 - 3i - 4i + 2i^2          6 - 7i - 2        4 - 7i                4    - 7i
---------------------          -----------        -------    OR     ---    -----   
         4 - i^2                  4 + 1              5                    5      5


The answer can be written either way. If they specify real part and imaginary part, the second option is correct.



abidemiokin

The result of the quotient b/a is 4/5 -7/5 i

Given the complex numbers a = 2 + i, and b = 3 – 2i, we are to get the value of the expression b/a by rationalizing

[tex]\frac{b}{a} = \frac{3-2i}{2+1}[/tex]

Rationalize the resulting quotient as shown:

[tex]=\frac{3-2i}{2+i}\times \frac{2-i}{2-i}\\ =\frac{(3-2i)(2-i)}{(2+i)(2-i)} \\=\frac{6-3i-4i+2i^2}{4-2i+2i-i^2} \\=\frac{6-7i-2}{4+1} \\=\frac{4-7i}{5}[/tex]

Hence the result of the quotient b/a is 4/5 -7/5 i

Learn more on complex numbers here: https://brainly.com/question/12375854

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