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Question

If z=3+4i and zw=14+2i, then

A
argw=π4
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B
argw=π4
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C
|w|=22
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D
|w|=4
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Solution

The correct option is C |w|=22
zw=14+2iz=3+4i(3+4i)w=14+2iw=14+2i3+4iw=(14+2i)(34i)(3+4i)(34i)w=42+56i6i+89+16w=50+50i25w=2+2i|w|=22+22=22tanα=(22)=π4

As w lies in first quadrant, so
argw=α=π4

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