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Question

logπ4(1+3i) can be expressed in cartesian form as

A
ln2+(2π3)ilnπ4
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B
ln2(2π3)ilnπ4
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C
ln2+(π3)ilnπ2
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D
ln2(2π3)ilnπ2
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Solution

The correct option is A ln2+(2π3)ilnπ4
We know that,
ln(z)=ln(|z|)+iarg(z)

For z=1+3i;|z|=2,arg(z)=ππ3=2π3

logπ4(1+3i)=ln(1+3i)lnπ4=ln2+2π3ilnπ4

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