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Question

Question: The statement \(x = - 1,y = 3\) is true for....

The statement x=−1,y=3x = - 1,y = 3 is true for.

A

x=1,y=3x = 1,y = 3

B

x=−1,y=−3x = - 1,y = - 3

C

x=1,x = 1,

D

y=3y = 3

Answer

y=3y = 3

Explanation

Solution

a=cos⁡θ+isin⁡θ.a = \cos\theta + i\sin\theta. defined if and only if its imaginary parts must be equal to zero, i.e. 1+a1−a=(1+cos⁡θ)+isin⁡θ(1−cos⁡θ)−isin⁡θ.\frac{1 + a}{1 - a} = \frac{(1 + \cos\theta) + i\sin\theta}{(1 - \cos\theta) - i\sin\theta}. So,1+a1−a=(1+cos⁡θ)+isin⁡θ(1−cos⁡θ)−isin⁡θ×(1−cos⁡θ)+isin⁡θ(1−cos⁡θ)+isin⁡θ\frac{1 + a}{1 - a} = \frac{(1 + \cos\theta) + i\sin\theta}{(1 - \cos\theta) - i\sin\theta} \times \frac{(1 - \cos\theta) + i\sin\theta}{(1 - \cos\theta) + i\sin\theta}.