(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

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

Add 1 and 1.

(i25)2

(i25)2

Rewrite i2 as -1.

(-15)2

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

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