1
Question
If z1=2−i,z2=−2+i,find
Re(z1z2¯z1)
Re(z1z2¯z1)
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Solution
Here z1=2−i,z2=−2+i
We have to find Re(z1z2¯z1),¯z1=2+i
Now z1z2=(2−i)(−2+i)=2(−2+i)−i(−2+i)=−4+2i+2i−i2=−4+4i−(−1)=−3+4i
z1z2¯z1=−3+4i2+i=(−3+4i)(2−i)(2+i)(2−i)=−3(2−i)+4i(2−i)22−(i2)=−6+3i+8i−4i24+1=−6+4+11i5=−25+115i∴Re(z1z2¯z1)=−25
Here z1=2−i,z2=−2+i
We have to find Re(z1z2¯z1),¯z1=2+i
Now z1z2=(2−i)(−2+i)=2(−2+i)−i(−2+i)=−4+2i+2i−i2=−4+4i−(−1)=−3+4i
z1z2¯z1=−3+4i2+i=(−3+4i)(2−i)(2+i)(2−i)=−3(2−i)+4i(2−i)22−(i2)=−6+3i+8i−4i24+1=−6+4+11i5=−25+115i∴Re(z1z2¯z1)=−25
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