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

Math
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.
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Combine.
(3-2i)(5+2i)(5-2i)(5+2i)
Simplify the numerator.
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Expand (3-2i)(5+2i) using the FOIL Method.
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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.
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Simplify each term.
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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).
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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)
Add 15 and 4.
19+6i-10i(5-2i)(5+2i)
Subtract 10i from 6i.
19-4i(5-2i)(5+2i)
19-4i(5-2i)(5+2i)
19-4i(5-2i)(5+2i)
Simplify the denominator.
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Expand (5-2i)(5+2i) using the FOIL Method.
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Apply the distributive property.
19-4i5(5+2i)-2i(5+2i)
Apply the distributive property.
19-4i5⋅5+5(2i)-2i(5+2i)
Apply the distributive property.
19-4i5⋅5+5(2i)-2i⋅5-2i(2i)
19-4i5⋅5+5(2i)-2i⋅5-2i(2i)
Simplify.
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Multiply 5 by 5.
19-4i25+5(2i)-2i⋅5-2i(2i)
Multiply 2 by 5.
19-4i25+10i-2i⋅5-2i(2i)
Multiply 5 by -2.
19-4i25+10i-10i-2i(2i)
Multiply 2 by -2.
19-4i25+10i-10i-4ii
Raise i to the power of 1.
19-4i25+10i-10i-4(i1i)
Raise i to the power of 1.
19-4i25+10i-10i-4(i1i1)
Use the power rule aman=am+n to combine exponents.
19-4i25+10i-10i-4i1+1
Add 1 and 1.
19-4i25+10i-10i-4i2
Subtract 10i from 10i.
19-4i25+0-4i2
Add 25 and 0.
19-4i25-4i2
19-4i25-4i2
Simplify each term.
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Rewrite i2 as -1.
19-4i25-4⋅-1
Multiply -4 by -1.
19-4i25+4
19-4i25+4
Add 25 and 4.
19-4i29
19-4i29
19-4i29
Split the fraction 19-4i29 into two fractions.
1929+-4i29
Move the negative in front of the fraction.
1929-4i29
Rewrite in Standard Form (3-2i)/(5-2i)

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