Question

Is the statement "The conjugate of 1+6i is 6+1i" true or false?

a) True
b) False
c) True, if the imaginary parts are swapped.
d) False, it's the same as the original.

Answer 1

The statement is false; the conjugate of a complex number is obtained by negating the imaginary part, making the conjugate of 1+6i equal to 1-6i.

Step-by-step explanation:

The statement "The conjugate of 1+6i is 6+1i" is false. The conjugate of a complex number is found by changing the sign of the imaginary part while keeping the real part the same. Therefore, the conjugate of 1+6i is 1-6i, not 6+1i. This idea is rooted in the property of complex numbers where the product of a complex number and its conjugate gives a real number, specifically the sum of the squares of the real and imaginary parts: A* A = (a + ib) (a − ib) = a² + b².