gaokao 2010 Q2

gaokao · China · shanghai-science Complex Numbers Arithmetic Complex Division/Multiplication Simplification

2. If the complex number $z = 1 - 2 i$ ($i$ is the imaginary unit), then $z \cdot \bar { z } + z =$ $\_\_\_\_$ $6 - 2i$.
Analysis: This examines basic operations with complex numbers. $z \cdot \bar { z } + z = ( 1 - 2 i ) ( 1 + 2 i ) + 1 - 2 i = 6 - 2 i$

(5 points) For plane vectors $\overrightarrow { a } , \overrightarrow { b }$, given $\overrightarrow { a } = ( 4,3 ) , 2 \overrightarrow { a } + \overrightarrow { b } = ( 3,18 )$, the cosine of the angle between $\overrightarrow { a }$ and $\overrightarrow { b }$ equals

2. If the complex number $z = 1 - 2 i$ ($i$ is the imaginary unit), then $z \cdot \bar { z } + z =$ $\_\_\_\_$ $6 - 2i$.

Analysis: This examines basic operations with complex numbers. $z \cdot \bar { z } + z = ( 1 - 2 i ) ( 1 + 2 i ) + 1 - 2 i = 6 - 2 i$

Paper Questions

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