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Q.

If z1=3+i3  and z2=3+i, then the complex number (z1z2)50 lies in the

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a

First quadrant

b

Second quadrant

c

Third quadrant

d

Fourth quadrant

answer is A.

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Detailed Solution

Given that z1=3+i3 And z2=3+i,z1z250=3+i33+i50              =3(1+i)3+i225=3(2i)3−1+23i25              =3i1+3i25=325i25(−2ω2)25  −i.ω(32)25=−i(−1+3i2)(32)25=(32)25(32+12i)Hence,z1z250 lies in the first quadrant as both real and imaginary parts of this number are positive.
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