# Simplify (i square root of -5)^2

(i-5)2
Rewrite -5 as -1(5).
(i-1(5))2
Rewrite -1(5) as -1⋅5.
(i(-1⋅5))2
Rewrite -1 as i.
(i(i⋅5))2
Multiply i(i5).
Raise i to the power of 1.
(i1i5)2
Raise i to the power of 1.
(i1i15)2
Use the power rule aman=am+n to combine exponents.
(i1+15)2
(i25)2
(i25)2
Rewrite i2 as -1.
(-15)2
Simplify the expression.
Rewrite -15 as -5.
(-5)2
Apply the product rule to -5.
(-1)252
Raise -1 to the power of 2.
152
Multiply 52 by 1.
52
52
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
(512)2
Apply the power rule and multiply exponents, (am)n=amn.
512⋅2
Combine 12 and 2.
522
Cancel the common factor of 2.
Cancel the common factor.
522
Divide 1 by 1.
51
51
Evaluate the exponent.
5
5
Simplify (i square root of -5)^2