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Question

If w=9+3i12i, then

A
|w|=32
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B
argw=π4
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C
|w|=2
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D
argw=3π4
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Solution

The correct option is D argw=3π4
w=9+3i12iw=(9+3i)(1+2i)(12i)(1+2i)w=918i+3i61+4w=1515i5=33i|w|=|33i|=(3)2+(3)2|w|=32

Now,
tanα=(33)=1
α=π4
As w lies in third quadrant, so
argw=(πα)=(ππ4)argw=3π4

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