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Multiple Choice
Find the product of the given complex number and its conjugate. −7−i
A
50
B
14
C
49
D
1
Verified step by step guidance
1
Identify the given complex number, which is \(-7 - i\).
Determine the conjugate of the complex number. The conjugate of a complex number \(a + bi\) is \(a - bi\). Therefore, the conjugate of \(-7 - i\) is \(-7 + i\).
Set up the expression for the product of the complex number and its conjugate: \((-7 - i)(-7 + i)\).
Apply the formula for the product of a complex number and its conjugate: \((a + bi)(a - bi) = a^2 + b^2\). Here, \(a = -7\) and \(b = 1\).
Calculate \(a^2 + b^2\) using the values of \(a\) and \(b\): \((-7)^2 + (1)^2\).