csat-suneung 2009 Q22

csat-suneung · South-Korea · csat__math-humanities 4 marks Complex Numbers Arithmetic Probability Involving Complex Number Conditions
When rolling a die twice, let the outcomes be $m$ and $n$ in order. If the probability that $i ^ { m } \cdot ( - i ) ^ { n } = 1$ is $\frac { q } { p }$, find the value of $p + q$. (Here, $i = \sqrt { - 1 }$ and $p , q$ are coprime natural numbers.) [4 points] 
When rolling a die twice, let the outcomes be $m$ and $n$ in order. If the probability that $i ^ { m } \cdot ( - i ) ^ { n } = 1$ is $\frac { q } { p }$, find the value of $p + q$. (Here, $i = \sqrt { - 1 }$ and $p , q$ are coprime natural numbers.) [4 points]
Paper Questions
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