a+i b form of the complex number (1+2 i ) (1+3 i )(2+i)^ -1 is - Vidyadip

MCQ

$a+i b$ form of the complex number $\left(1+\frac{2}{i}\right)\left(1+\frac{3}{i}\right)(2+i)^{-1}$ is

✓
$-3- i$
B
$-3+i$
C
$-5- i$
D
$-5+i$

✓

Answer

Correct option: A.

$-3- i$

(A)
$\left(1+\frac{2}{ i }\right)\left(1+\frac{3}{ i }\right)(2+ i )^{-1}=\frac{( i +2)( i +3)}{ i ^2(2+ i )}$
$=\frac{( i +3)}{ i ^2}$
$=-3- i$

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