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

Math
2i4-5i
Multiply the numerator and denominator of 2i4-5i by the conjugate of 4-5i to make the denominator real.
2i4-5i⋅4+5i4+5i
Multiply.
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Combine.
2i(4+5i)(4-5i)(4+5i)
Simplify the numerator.
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Apply the distributive property.
2i⋅4+2i(5i)(4-5i)(4+5i)
Multiply 4 by 2.
8i+2i(5i)(4-5i)(4+5i)
Multiply 2i(5i).
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Multiply 5 by 2.
8i+10ii(4-5i)(4+5i)
Raise i to the power of 1.
8i+10(i1i)(4-5i)(4+5i)
Raise i to the power of 1.
8i+10(i1i1)(4-5i)(4+5i)
Use the power rule aman=am+n to combine exponents.
8i+10i1+1(4-5i)(4+5i)
Add 1 and 1.
8i+10i2(4-5i)(4+5i)
8i+10i2(4-5i)(4+5i)
Simplify each term.
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Rewrite i2 as -1.
8i+10⋅-1(4-5i)(4+5i)
Multiply 10 by -1.
8i-10(4-5i)(4+5i)
8i-10(4-5i)(4+5i)
Reorder 8i and -10.
-10+8i(4-5i)(4+5i)
-10+8i(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.
-10+8i4(4+5i)-5i(4+5i)
Apply the distributive property.
-10+8i4⋅4+4(5i)-5i(4+5i)
Apply the distributive property.
-10+8i4⋅4+4(5i)-5i⋅4-5i(5i)
-10+8i4⋅4+4(5i)-5i⋅4-5i(5i)
Simplify.
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Multiply 4 by 4.
-10+8i16+4(5i)-5i⋅4-5i(5i)
Multiply 5 by 4.
-10+8i16+20i-5i⋅4-5i(5i)
Multiply 4 by -5.
-10+8i16+20i-20i-5i(5i)
Multiply 5 by -5.
-10+8i16+20i-20i-25ii
Raise i to the power of 1.
-10+8i16+20i-20i-25(i1i)
Raise i to the power of 1.
-10+8i16+20i-20i-25(i1i1)
Use the power rule aman=am+n to combine exponents.
-10+8i16+20i-20i-25i1+1
Add 1 and 1.
-10+8i16+20i-20i-25i2
Subtract 20i from 20i.
-10+8i16+0-25i2
Add 16 and 0.
-10+8i16-25i2
-10+8i16-25i2
Simplify each term.
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Rewrite i2 as -1.
-10+8i16-25⋅-1
Multiply -25 by -1.
-10+8i16+25
-10+8i16+25
Add 16 and 25.
-10+8i41
-10+8i41
-10+8i41
Split the fraction -10+8i41 into two fractions.
-1041+8i41
Move the negative in front of the fraction.
-1041+8i41
Rewrite in Standard Form (2i)/(4-5i)

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