(5+3i)(5-3i)

Apply the distributive property.

5(5-3i)+3i(5-3i)

Apply the distributive property.

55+5(-3i)+3i(5-3i)

Apply the distributive property.

55+5(-3i)+3i5+3i(-3i)

55+5(-3i)+3i5+3i(-3i)

Simplify each term.

Combine using the product rule for radicals.

5⋅5+5(-3i)+3i5+3i(-3i)

Multiply 5 by 5.

25+5(-3i)+3i5+3i(-3i)

Rewrite 25 as 52.

52+5(-3i)+3i5+3i(-3i)

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

5+5(-3i)+3i5+3i(-3i)

Move -3 to the left of 5.

5-3⋅5i+3i5+3i(-3i)

Multiply 3i(-3i).

Multiply -3 by 3.

5-35i+3i5-9ii

Raise i to the power of 1.

5-35i+3i5-9(i1i)

Raise i to the power of 1.

5-35i+3i5-9(i1i1)

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

5-35i+3i5-9i1+1

Add 1 and 1.

5-35i+3i5-9i2

5-35i+3i5-9i2

Rewrite i2 as -1.

5-35i+3i5-9⋅-1

Multiply -9 by -1.

5-35i+3i5+9

5-35i+3i5+9

Add 5 and 9.

-35i+3i5+14

Reorder the factors of -35i.

-3i5+3i5+14

Add -3i5 and 3i5.

0+14

Add 0 and 14.

14

14

Simplify ( square root of 5+3i)( square root of 5-3i)