Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
Question
Find a and b if $:abi = 3a – b + 12i$
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Answer
$abi = 3a – b + 12i $
$\therefore 0 + abi = (3a – b) + 12i$
Equating real and imaginary parts,
we get $3a – b = 0 $
$\therefore 3a = b …..(i)$ and $ab = 12$
$\therefore b=\frac{12}{a}$
Substituting $b=\frac{12}{a}$ in (i), we get
$3 a=\frac{12}{a}$
$3 a^2=12$
$a^2=4$
$a= \pm 2$
When $a=2, b=\frac{12}{a}=\frac{12}{2}=6$
When $a=-2, b=\frac{12}{a}=\frac{12}{-2}=-6$
$\therefore a = 2$ and $b = 6$ or $a = -2$ and $b = -6$
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