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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 options are
A argw=π4
C |w|=22
zw=14+2i
z=3+4i
(3+4i)w=14+2i
w=14+2i3+4i
w=(14+2i)(34i)(3+4i)(34i)
w=42+56i6i+89+16
w=50+50i25
w=2+2i
|w|=22+22=22
tanα=(|2||2|)=π4
As w lies in first quadrant So,
argw=α=π4

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