# Rewrite in Standard Form (3+2i)/(5-2i)

3+2i5-2i
Multiply the numerator and denominator of 3+2i5-2i by the conjugate of 5-2i to make the denominator real.
3+2i5-2i⋅5+2i5+2i
Multiply.
Combine.
(3+2i)(5+2i)(5-2i)(5+2i)
Simplify the numerator.
Expand (3+2i)(5+2i) using the FOIL Method.
Apply the distributive property.
3(5+2i)+2i(5+2i)(5-2i)(5+2i)
Apply the distributive property.
3⋅5+3(2i)+2i(5+2i)(5-2i)(5+2i)
Apply the distributive property.
3⋅5+3(2i)+2i⋅5+2i(2i)(5-2i)(5+2i)
3⋅5+3(2i)+2i⋅5+2i(2i)(5-2i)(5+2i)
Simplify and combine like terms.
Simplify each term.
Multiply 3 by 5.
15+3(2i)+2i⋅5+2i(2i)(5-2i)(5+2i)
Multiply 2 by 3.
15+6i+2i⋅5+2i(2i)(5-2i)(5+2i)
Multiply 5 by 2.
15+6i+10i+2i(2i)(5-2i)(5+2i)
Multiply 2i(2i).
Multiply 2 by 2.
15+6i+10i+4ii(5-2i)(5+2i)
Raise i to the power of 1.
15+6i+10i+4(i1i)(5-2i)(5+2i)
Raise i to the power of 1.
15+6i+10i+4(i1i1)(5-2i)(5+2i)
Use the power rule aman=am+n to combine exponents.
15+6i+10i+4i1+1(5-2i)(5+2i)
Add 1 and 1.
15+6i+10i+4i2(5-2i)(5+2i)
15+6i+10i+4i2(5-2i)(5+2i)
Rewrite i2 as -1.
15+6i+10i+4⋅-1(5-2i)(5+2i)
Multiply 4 by -1.
15+6i+10i-4(5-2i)(5+2i)
15+6i+10i-4(5-2i)(5+2i)
Subtract 4 from 15.
11+6i+10i(5-2i)(5+2i)
Add 6i and 10i.
11+16i(5-2i)(5+2i)
11+16i(5-2i)(5+2i)
11+16i(5-2i)(5+2i)
Simplify the denominator.
Expand (5-2i)(5+2i) using the FOIL Method.
Apply the distributive property.
11+16i5(5+2i)-2i(5+2i)
Apply the distributive property.
11+16i5⋅5+5(2i)-2i(5+2i)
Apply the distributive property.
11+16i5⋅5+5(2i)-2i⋅5-2i(2i)
11+16i5⋅5+5(2i)-2i⋅5-2i(2i)
Simplify.
Multiply 5 by 5.
11+16i25+5(2i)-2i⋅5-2i(2i)
Multiply 2 by 5.
11+16i25+10i-2i⋅5-2i(2i)
Multiply 5 by -2.
11+16i25+10i-10i-2i(2i)
Multiply 2 by -2.
11+16i25+10i-10i-4ii
Raise i to the power of 1.
11+16i25+10i-10i-4(i1i)
Raise i to the power of 1.
11+16i25+10i-10i-4(i1i1)
Use the power rule aman=am+n to combine exponents.
11+16i25+10i-10i-4i1+1
Add 1 and 1.
11+16i25+10i-10i-4i2
Subtract 10i from 10i.
11+16i25+0-4i2
Add 25 and 0.
11+16i25-4i2
11+16i25-4i2
Simplify each term.
Rewrite i2 as -1.
11+16i25-4⋅-1
Multiply -4 by -1.
11+16i25+4
11+16i25+4
Add 25 and 4.
11+16i29
11+16i29
11+16i29
Split the fraction 11+16i29 into two fractions.
1129+16i29
Rewrite in Standard Form (3+2i)/(5-2i)

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