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Statement-1: Two lines \( a \bar{z}+\bar{a} z+b=0=0, a_{1} \bar{z} \) \( +\bar{a}_{1} z+b_{1}=0 \) (where \( a, a_{1} \in \mathbf{C}, a, a_{1} \neq 0 \) and \( \left.b, b_{1} \in \mathbf{R}\right) \) are parallel if and only if \( \frac{a}{a_{1}} \) is real.
Statement-2: Two lines \( a \bar{z}+\bar{a} z+b=0, a_{1} \bar{z}+ \) \( \bar{a}_{1} z+b_{1}=0 \) (where \( a, a_{1} \in \mathbf{C}, a, a_{1} \neq 0 \) and \( b \), \( \left.b_{1} \in \mathbf{R}\right) \) are perpendicular if and only if \( \frac{a}{a_{1}} \) is purely imaginary.
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