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Question

If z1=2i,z2=2+i,find
Re(z1z2¯z1)

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Solution

Here z1=2i,z2=2+i

We have to find Re(z1z2¯z1),¯z1=2+i

Now z1z2=(2i)(2+i)=2(2+i)i(2+i)=4+2i+2ii2=4+4i(1)=3+4i

z1z2¯z1=3+4i2+i=(3+4i)(2i)(2+i)(2i)=3(2i)+4i(2i)22(i2)=6+3i+8i4i24+1=6+4+11i5=25+115iRe(z1z2¯z1)=25


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