Write in Standard Form (-7i)/(5-4i)

Math
-7i5-4i
Multiply the numerator and denominator of -7i5-4i by the conjugate of 5-4i to make the denominator real.
-7i5-4i⋅5+4i5+4i
Multiply.
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Combine.
-7i(5+4i)(5-4i)(5+4i)
Simplify the numerator.
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Apply the distributive property.
-7i⋅5-7i(4i)(5-4i)(5+4i)
Multiply 5 by -7.
-35i-7i(4i)(5-4i)(5+4i)
Multiply -7i(4i).
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Multiply 4 by -7.
-35i-28ii(5-4i)(5+4i)
Raise i to the power of 1.
-35i-28(i1i)(5-4i)(5+4i)
Raise i to the power of 1.
-35i-28(i1i1)(5-4i)(5+4i)
Use the power rule aman=am+n to combine exponents.
-35i-28i1+1(5-4i)(5+4i)
Add 1 and 1.
-35i-28i2(5-4i)(5+4i)
-35i-28i2(5-4i)(5+4i)
Simplify each term.
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Rewrite i2 as -1.
-35i-28⋅-1(5-4i)(5+4i)
Multiply -28 by -1.
-35i+28(5-4i)(5+4i)
-35i+28(5-4i)(5+4i)
Reorder -35i and 28.
28-35i(5-4i)(5+4i)
28-35i(5-4i)(5+4i)
Simplify the denominator.
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Expand (5-4i)(5+4i) using the FOIL Method.
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Apply the distributive property.
28-35i5(5+4i)-4i(5+4i)
Apply the distributive property.
28-35i5⋅5+5(4i)-4i(5+4i)
Apply the distributive property.
28-35i5⋅5+5(4i)-4i⋅5-4i(4i)
28-35i5⋅5+5(4i)-4i⋅5-4i(4i)
Simplify.
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Multiply 5 by 5.
28-35i25+5(4i)-4i⋅5-4i(4i)
Multiply 4 by 5.
28-35i25+20i-4i⋅5-4i(4i)
Multiply 5 by -4.
28-35i25+20i-20i-4i(4i)
Multiply 4 by -4.
28-35i25+20i-20i-16ii
Raise i to the power of 1.
28-35i25+20i-20i-16(i1i)
Raise i to the power of 1.
28-35i25+20i-20i-16(i1i1)
Use the power rule aman=am+n to combine exponents.
28-35i25+20i-20i-16i1+1
Add 1 and 1.
28-35i25+20i-20i-16i2
Subtract 20i from 20i.
28-35i25+0-16i2
Add 25 and 0.
28-35i25-16i2
28-35i25-16i2
Simplify each term.
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Rewrite i2 as -1.
28-35i25-16⋅-1
Multiply -16 by -1.
28-35i25+16
28-35i25+16
Add 25 and 16.
28-35i41
28-35i41
28-35i41
Split the fraction 28-35i41 into two fractions.
2841+-35i41
Move the negative in front of the fraction.
2841-35i41
Write in Standard Form (-7i)/(5-4i)

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