Question

If
z 1 = 2 - i
z 2 = -2 + i
Re (z1z2/ z1)
​

Answer 1

Answer:

$\sf{Re(\dfrac{z_{1}z_{2}}{z_{1}})=-2}$

Given:

$\sf{\leadsto{z_{1}=2-i}}$

$\sf{\leadsto{z_{2}=-2+i}}$

To find:

$\sf{Re(\dfrac{z_{1}z_{2}}{z_{1}})}$

Solution:

$\sf{\leadsto{\dfrac{z_{1}z_{2}}{z_{1}}}}$

$\sf{\leadsto{z_{2}}}$

$\sf{But, \ z_{2}=-2+i}$

$\sf{\leadsto{-2+i}}$

$\sf\purple{\tt{\therefore{Re(\dfrac{z_{1}z_{2}}{z_{1}})=-2}}}$

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$\sf\blue{Extra \ information:}$

$\sf{i^{2}=-1}$

$\sf{i^{3}=-i}$

$\sf{i^{4}=1}$