(6-5i)(6+5i)

Apply the distributive property.

6(6+5i)-5i(6+5i)

Apply the distributive property.

66+65i-5i(6+5i)

Apply the distributive property.

66+65i-5i6-5i5i

66+65i-5i6-5i5i

Simplify each term.

Combine using the product rule for radicals.

6⋅6+65i-5i6-5i5i

Multiply 6 by 6.

36+65i-5i6-5i5i

Rewrite 36 as 62.

62+65i-5i6-5i5i

Pull terms out from under the radical, assuming positive real numbers.

6+65i-5i6-5i5i

Combine using the product rule for radicals.

6+6(5i)-5i6-5i5i

Multiply 6 by 5.

6+30i-5i6-5i5i

Multiply -5i6.

Combine using the product rule for radicals.

6+30i-6(5i)-5i5i

Multiply 6 by 5.

6+30i-30i-5i5i

6+30i-30i-5i5i

Multiply -5i5i.

Raise 5i to the power of 1.

6+30i-30i-(5i15i)

Raise 5i to the power of 1.

6+30i-30i-(5i15i1)

Use the power rule aman=am+n to combine exponents.

6+30i-30i-5i1+1

Add 1 and 1.

6+30i-30i-5i2

6+30i-30i-5i2

Rewrite 5i2 as 5i.

Use axn=axn to rewrite 5i as (5i)12.

6+30i-30i-((5i)12)2

Apply the power rule and multiply exponents, (am)n=amn.

6+30i-30i-(5i)12⋅2

Combine 12 and 2.

6+30i-30i-(5i)22

Cancel the common factor of 2.

Cancel the common factor.

6+30i-30i-(5i)22

Divide 1 by 1.

6+30i-30i-(5i)1

6+30i-30i-(5i)1

Simplify.

6+30i-30i-(5i)

6+30i-30i-(5i)

Multiply 5 by -1.

6+30i-30i-5i

6+30i-30i-5i

Subtract 30i from 30i.

6+0-5i

Add 6 and 0.

6-5i

6-5i

Simplify ( square root of 6- square root of 5i)( square root of 6+ square root of 5i)