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CBSE Class 10 Answered

For any two complex numbers z1 and z2, show that Re(z1z2) = Rez1 Rez2– Imz1Imz2

Asked by umiuri | 01 Jul, 2021, 09:21: AM
Expert Answer
Let z1 = a + ib and z2 = c + id
straight z subscript 1 straight z subscript 2 equals open parentheses straight a plus ib close parentheses open parentheses straight c plus id close parentheses equals ac minus bd plus straight i open parentheses ad plus bc close parentheses
Re open parentheses straight z subscript 1 straight z subscript 2 close parentheses equals ac minus bd
Re open parentheses straight z subscript 1 close parentheses Re open parentheses straight z subscript 2 close parentheses minus Im open parentheses straight z subscript 1 close parentheses Im open parentheses straight z subscript 2 close parentheses equals ac minus bd
Hence comma space Re open parentheses straight z subscript 1 straight z subscript 2 close parentheses equals Re open parentheses straight z subscript 1 close parentheses Re open parentheses straight z subscript 2 close parentheses minus Im open parentheses straight z subscript 1 close parentheses Im open parentheses straight z subscript 2 close parentheses
Answered by Renu Varma | 01 Jul, 2021, 11:13: AM
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