Rewrite in Standard Form (3-2i)/(4-5i)

Math
3-2i4-5i
Multiply the numerator and denominator of 3-2i4-5i by the conjugate of 4-5i to make the denominator real.
3-2i4-5i⋅4+5i4+5i
Multiply.
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Combine.
(3-2i)(4+5i)(4-5i)(4+5i)
Simplify the numerator.
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Expand (3-2i)(4+5i) using the FOIL Method.
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Apply the distributive property.
3(4+5i)-2i(4+5i)(4-5i)(4+5i)
Apply the distributive property.
3⋅4+3(5i)-2i(4+5i)(4-5i)(4+5i)
Apply the distributive property.
3⋅4+3(5i)-2i⋅4-2i(5i)(4-5i)(4+5i)
3⋅4+3(5i)-2i⋅4-2i(5i)(4-5i)(4+5i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 3 by 4.
12+3(5i)-2i⋅4-2i(5i)(4-5i)(4+5i)
Multiply 5 by 3.
12+15i-2i⋅4-2i(5i)(4-5i)(4+5i)
Multiply 4 by -2.
12+15i-8i-2i(5i)(4-5i)(4+5i)
Multiply -2i(5i).
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Multiply 5 by -2.
12+15i-8i-10ii(4-5i)(4+5i)
Raise i to the power of 1.
12+15i-8i-10(i1i)(4-5i)(4+5i)
Raise i to the power of 1.
12+15i-8i-10(i1i1)(4-5i)(4+5i)
Use the power rule aman=am+n to combine exponents.
12+15i-8i-10i1+1(4-5i)(4+5i)
Add 1 and 1.
12+15i-8i-10i2(4-5i)(4+5i)
12+15i-8i-10i2(4-5i)(4+5i)
Rewrite i2 as -1.
12+15i-8i-10⋅-1(4-5i)(4+5i)
Multiply -10 by -1.
12+15i-8i+10(4-5i)(4+5i)
12+15i-8i+10(4-5i)(4+5i)
Add 12 and 10.
22+15i-8i(4-5i)(4+5i)
Subtract 8i from 15i.
22+7i(4-5i)(4+5i)
22+7i(4-5i)(4+5i)
22+7i(4-5i)(4+5i)
Simplify the denominator.
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Expand (4-5i)(4+5i) using the FOIL Method.
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Apply the distributive property.
22+7i4(4+5i)-5i(4+5i)
Apply the distributive property.
22+7i4⋅4+4(5i)-5i(4+5i)
Apply the distributive property.
22+7i4⋅4+4(5i)-5i⋅4-5i(5i)
22+7i4⋅4+4(5i)-5i⋅4-5i(5i)
Simplify.
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Multiply 4 by 4.
22+7i16+4(5i)-5i⋅4-5i(5i)
Multiply 5 by 4.
22+7i16+20i-5i⋅4-5i(5i)
Multiply 4 by -5.
22+7i16+20i-20i-5i(5i)
Multiply 5 by -5.
22+7i16+20i-20i-25ii
Raise i to the power of 1.
22+7i16+20i-20i-25(i1i)
Raise i to the power of 1.
22+7i16+20i-20i-25(i1i1)
Use the power rule aman=am+n to combine exponents.
22+7i16+20i-20i-25i1+1
Add 1 and 1.
22+7i16+20i-20i-25i2
Subtract 20i from 20i.
22+7i16+0-25i2
Add 16 and 0.
22+7i16-25i2
22+7i16-25i2
Simplify each term.
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Rewrite i2 as -1.
22+7i16-25⋅-1
Multiply -25 by -1.
22+7i16+25
22+7i16+25
Add 16 and 25.
22+7i41
22+7i41
22+7i41
Split the fraction 22+7i41 into two fractions.
2241+7i41
Rewrite in Standard Form (3-2i)/(4-5i)

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