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Question

If z1=1+2i and z2=3+5i, then the real part of z2¯z1z2 is


A

-3117

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B

1722

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C

-1731

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D

2217

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Solution

The correct option is D

2217


Explanation for the correct option.

Find the real part of z2¯z1z2.

For the function z2=3+5i the conjugate is given as: z2¯=3-5i.

So substitute z1=1+2i, z2¯=3-5i, and z2=3+5i in z2¯z1z2 and simplify.

z2¯z1z2=3-5i1+2i3+5i=3+6i-5i-10i23+5i=3+i-10×-13+5ii2=-1=3+i+103+5i=13+i3+5i

Now multiply the numerator and denominator by 3-5i.

13+i3-5i3+5i3-5i=39-65i+3i-5i29-25i2=39-62i-5×-19-25×-1i2=-1=39-62i+59+25=44-62i34=22-31i17=2217-31i17

Thus, z2¯z1z2=2217-31i17 and its real part is 2217.

Hence, the correct option is D.


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