Exercise 21
1 . In the following Argand diagram with the origin O , the point A and the point B represent the complex numbers �2
� 9i and 3� 3i respectively . The shape of ABCD is a rectangle such that AD � 2AB .
( a ) Write down
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( i ) Re ( 3�3i ) � Re ( �2 � 9i ) ;
( ii ) Im ( 3�3i ) � Im ( �2 � 9i ) .
( b ) Find the length of AB .
( c ) Hence , find the area of ABCD .
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2 . In the following Argand diagram with the origin O , the point A represents the complex numbers �18 � 10i . The shape of ABC is an equilateral triangle with the horizontal side AB � 20 .
( a ) Determine the complex numbers represented by ( i ) the point B ;
( ii ) the point C , giving the answer in exact value .
( b ) Find the area of ABC .
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