gaokao 2004 Q17

gaokao · China · shanghai-science Complex Numbers Arithmetic Solving Equations for Unknown Complex Numbers
17. (Total Score: 12 points) Given that the complex number $z _ { 1 }$ satisfies $( 1 + i ) z _ { 1 } = - 1 + 5 i$, and $z _ { 2 } = a - 2 - i$, where $i$ is the imaginary unit and $a \in \mathbb{R}$. If $\left| z _ { 1 } - \overline { z _ { 2 } } \right| < \left| z _ { 1 } \right|$, find the range of $a$. 
17. (Total Score: 12 points)\\
Given that the complex number $z _ { 1 }$ satisfies $( 1 + i ) z _ { 1 } = - 1 + 5 i$, and $z _ { 2 } = a - 2 - i$, where $i$ is the imaginary unit and $a \in \mathbb{R}$. If $\left| z _ { 1 } - \overline { z _ { 2 } } \right| < \left| z _ { 1 } \right|$, find the range of $a$.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22