The products of each pair of complex conjugates is 41
Given the pair of complex conjugates expressed as (4+5i)(4-5i)
[tex](4+5i)(4-5i)[/tex]
Expand the expression:
[tex]=(4+5i)(4-5i)\\= 4(4)-4(5i)+4(5i)-5i(5i)\\=16-20i+20i-25i^2\\=16-25i^2[/tex]
According to complex number, i² = -1
Substitute this into the result to have:
[tex]=16-25i^2\\=16-25(-1)\\=16+25\\=41[/tex]
Hence the products of each pair of complex conjugates is 41
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