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Question

If z=(1i)i, then the correct option(s) is/are

A
Re(z)=eπ4cos(log2)
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B
Im(z)=eπ4sin(12log2)
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C
Im(z)=eπ4sin(log2)
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D
Re(z)=eπ4cos(12log2)
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Solution

The correct options are
B Im(z)=eπ4sin(12log2)
D Re(z)=eπ4cos(12log2)
Let z=(1i)i, taking log on both sides
logz=iloge(1i)
=iloge(2(cosπ4isinπ4))
=iloge(2eiπ4)
=i12loge2+logeeiπ4
=i[12loge2iπ4]
=i2loge2π4
z=eπ4ei(log2)2
Re(z)=eπ4cos(12log2),Im(z)=eπ4sin(12log2)

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