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Express the following in the standard form $a + ib$: $\left ( -3+i \right )\left ( 4-2i \right )$

This is the third part of the multipart Q1.
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1 Answer

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  • $i^2=-1$.
  • In general,$i^{4n-3}=i$,$i^{4n-2}=-1$,$i^{4n}=1$
  • If $z=a+ib$ then ,
  • $\bar{z}=a-ib$
  • $\mid z\mid=\sqrt{a^2+b^2}$
  • $z^{-1}=\large\frac{a-ib}{a^2+b^2}$
  • $zz^{-1}=a^2+b^2$
  • Also $Re(z)=a,Im(z)=b$
$(-3+i)(4-2i)=-12+6i+4i-12i^2$
$\qquad\qquad\qquad\;\;=-12+10i+2$
$\qquad\qquad\qquad\;\;=-10+10i$
answered Jun 7, 2013 by sreemathi.v
 

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