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# Find the real and imaginary parts of the following complex numbers: $\left ( 2+i \right )\left ( 3-2i \right )$

This is the third part of the multi-part question Q2.
Can you answer this question?

## 1 Answer

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Toolbox:
• If $z=a+ib$ then ,
• $\bar{z}=a-ib$
• $\mid z\mid=\sqrt{a^2+b^2}$
• $z^{-1}=\large\frac{a-ib}{a^2+b^2}$
• $z^{-1}=\large\frac{a-ib}{a^2+b^2}$
• $z\bar{z}=a^2+b^2$
• Also $Re(z)=a,Im(z)=b$
• If $z_1=a+ib,z_2=c+id$
• $z_1z_2=(a+ib)(c+id)=(ac-bd)+i(ad+bc)$
• $\mid z_1z_2\mid=\mid z_1\mid\mid z_2\mid$
$z=(2+i)(3-2i)$
$(2+i)(3-2i)=(6+2)+i(3-4)$
$\qquad\qquad\quad\;\;\;=8-i$
$Re(z)=8$
$Im(z)=-1$
answered Jun 7, 2013

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