Apps. and Interpretation for IBDP Maths Ebook 2 | Page 73

www . seprodstore . com 63 6 Consider the complex numbers 1 cis ₆ z � � and 2 2 6cis ₃ z � � . ( a ) Express 1 2 zz in the form ( i ) cis r � ; ( ii ) i e r ^� . [ 3 ] ( b ) Hence , find the imaginary part of 1 2 zz . [ 2 ] ( a ) ( i ) 1 2 2 cis 6cis 6 3 zz � � � �� _� _�� _� � �� 1 2 2 ( 1 )( 6 ) cis ₆ ₃ zz � � � � � � � � � � ( M1 ) for valid approach 1 2 5 6cis ₆ zz � � A1 ( ii ) 5 _i 6 1 2 6 z z e � � A1 [ 3 ] ( b ) The imaginary part of 1 2 zz 5 6sin ₆ � � ( M1 ) for valid approach 3 � A1 [ 2 ] Example Solution 22 Paper 1 – Forms of Complex Numbers

www . seprodstore . com 63 6 Consider the complex numbers 1 cis ₆ z � � and 2 2 6cis ₃ z � � . ( a ) Express 1 2 zz in the form ( i ) cis r � ; ( ii ) i e r ^� . [ 3 ] ( b ) Hence , find the imaginary part of 1 2 zz . [ 2 ] ( a ) ( i ) 1 2 2 cis 6cis 6 3 zz � � � �� _� _�� _� � �� 1 2 2 ( 1 )( 6 ) cis ₆ ₃ zz � � � � � � � � � � ( M1 ) for valid approach 1 2 5 6cis ₆ zz � � A1 ( ii ) 5 _i 6 1 2 6 z z e � � A1 [ 3 ] ( b ) The imaginary part of 1 2 zz 5 6sin ₆ � � ( M1 ) for valid approach 3 � A1 [ 2 ] Example Solution 22 Paper 1 – Forms of Complex Numbers