{(-1)^0.5}^2 is considered as an error.
but why does (sqrt(-1))^2 equal -1?
and does it mean this equation {(-1)^0.5}^2={(-1)^2}^0.5 is not valid?
+128707 {(-1)^0.5}^2={(-1)^2}^0.5
This isn't triue......remember that sqrt(-1) is defined as " i " → i^2 = -1
So....using the order of operations on the left side results in :
[ i ] ^2 = -1
But, using the order of operations on the right results in :
[ 1 ] ^0.5 = sqrt (1) = 1
The problem lies in the way the order of operations are performed...... in the first instance, we are squaring a "complex" number, but in the second, we are taking the square root of a real number......
+128707 {(-1)^0.5}^2={(-1)^2}^0.5
This isn't triue......remember that sqrt(-1) is defined as " i " → i^2 = -1
So....using the order of operations on the left side results in :
[ i ] ^2 = -1
But, using the order of operations on the right results in :
[ 1 ] ^0.5 = sqrt (1) = 1
The problem lies in the way the order of operations are performed...... in the first instance, we are squaring a "complex" number, but in the second, we are taking the square root of a real number......
