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

(5+3i)(5-3i)
Expand (5+3i)(5-3i) using the FOIL Method.
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 and combine like terms.
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
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
-35i+3i5+14
Reorder the factors of -35i.
-3i5+3i5+14