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

Math
-3i4-5i
Multiply the numerator and denominator of -3i4-5i by the conjugate of 4-5i to make the denominator real.
-3i4-5i⋅4+5i4+5i
Multiply.
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Combine.
-3i(4+5i)(4-5i)(4+5i)
Simplify the numerator.
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Apply the distributive property.
-3i⋅4-3i(5i)(4-5i)(4+5i)
Multiply 4 by -3.
-12i-3i(5i)(4-5i)(4+5i)
Multiply -3i(5i).
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Multiply 5 by -3.
-12i-15ii(4-5i)(4+5i)
Raise i to the power of 1.
-12i-15(i1i)(4-5i)(4+5i)
Raise i to the power of 1.
-12i-15(i1i1)(4-5i)(4+5i)
Use the power rule aman=am+n to combine exponents.
-12i-15i1+1(4-5i)(4+5i)
Add 1 and 1.
-12i-15i2(4-5i)(4+5i)
-12i-15i2(4-5i)(4+5i)
Simplify each term.
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Rewrite i2 as -1.
-12i-15⋅-1(4-5i)(4+5i)
Multiply -15 by -1.
-12i+15(4-5i)(4+5i)
-12i+15(4-5i)(4+5i)
Reorder -12i and 15.
15-12i(4-5i)(4+5i)
15-12i(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.
15-12i4(4+5i)-5i(4+5i)
Apply the distributive property.
15-12i4⋅4+4(5i)-5i(4+5i)
Apply the distributive property.
15-12i4⋅4+4(5i)-5i⋅4-5i(5i)
15-12i4⋅4+4(5i)-5i⋅4-5i(5i)
Simplify.
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Multiply 4 by 4.
15-12i16+4(5i)-5i⋅4-5i(5i)
Multiply 5 by 4.
15-12i16+20i-5i⋅4-5i(5i)
Multiply 4 by -5.
15-12i16+20i-20i-5i(5i)
Multiply 5 by -5.
15-12i16+20i-20i-25ii
Raise i to the power of 1.
15-12i16+20i-20i-25(i1i)
Raise i to the power of 1.
15-12i16+20i-20i-25(i1i1)
Use the power rule aman=am+n to combine exponents.
15-12i16+20i-20i-25i1+1
Add 1 and 1.
15-12i16+20i-20i-25i2
Subtract 20i from 20i.
15-12i16+0-25i2
Add 16 and 0.
15-12i16-25i2
15-12i16-25i2
Simplify each term.
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Rewrite i2 as -1.
15-12i16-25⋅-1
Multiply -25 by -1.
15-12i16+25
15-12i16+25
Add 16 and 25.
15-12i41
15-12i41
15-12i41
Split the fraction 15-12i41 into two fractions.
1541+-12i41
Move the negative in front of the fraction.
1541-12i41
Rewrite in Standard Form (-3i)/(4-5i)

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