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Complex Numbers(p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Complex Numbers(p-1)1 Mark
Question
Simplify the following and express in the form $a+i b$ : $(1+3 i) 2(3+i)$
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Answer

$(1+3 i)^2(3+i)$
$=\left(1+6 i+9 i^2\right)(3+i)$
$\left.=(1+6 i-9)(3+i) \ldots . . \cdot \because i^2=-1\right]$
$=(-8+6 i)(3+i)$
$=-24-8 i+18 i+6 i^2$
$=-24+10 i+6(-1)$
$=-24+10 i-6$
$=-30+10 i$

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