A) \[-2\]
B) \[-1/2\]
C) 2
D) cannot be determined
Correct Answer: A
Solution :
Let \[\omega ={{x}_{1}}+i{{y}_{1}}\] and \[z={{x}_{2}}+i{{y}_{2}}\] Now \[(1+2i)({{x}_{1}}+i{{y}_{1}})\,\] is real \[\Rightarrow \,2{{x}_{1}}+{{y}_{1}}=0\] \[\Rightarrow \,2{{x}_{2}}+{{y}_{2}}=0\] \[\therefore \,\,2{{x}_{1}}+{{y}_{1}}=2{{x}_{2}}+{{y}_{2}}\] \[\Rightarrow \,-2({{x}_{2}}-{{x}_{1}})={{y}_{2}}-{{y}_{1}}\] \[\Rightarrow \,\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=-2\]
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