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Question

If sinθ=(z1i), where z is non real, θ represents angle of a triangle, then

A
Re(z)=1,Im(z)=2
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B
Re(z)=1,1Im(z)1
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C
Re(z)+Im(z)=0
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D
Re(z)=0,Im(z)=1
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Solution

The correct option is B Re(z)=1,1Im(z)1
If θ represents angle of a triangle, then sinθ must be real.
z1i will be real

Let z=x+iy, then
z1i=(x+iy)1i
=(x1)+iyi=(x1)ii×i+y
=yi(x1)

For yi(x1) to be real, x must be equal to 1
then sinθ=y exists if 1y1

Re(z)=1 and 1Im(z)1

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