Rewrite in Standard Form (4-7i)/(3+4i)

Math
4-7i3+4i
Multiply the numerator and denominator of 4-7i3+4i by the conjugate of 3+4i to make the denominator real.
4-7i3+4i⋅3-4i3-4i
Multiply.
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Combine.
(4-7i)(3-4i)(3+4i)(3-4i)
Simplify the numerator.
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Expand (4-7i)(3-4i) using the FOIL Method.
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Apply the distributive property.
4(3-4i)-7i(3-4i)(3+4i)(3-4i)
Apply the distributive property.
4⋅3+4(-4i)-7i(3-4i)(3+4i)(3-4i)
Apply the distributive property.
4⋅3+4(-4i)-7i⋅3-7i(-4i)(3+4i)(3-4i)
4⋅3+4(-4i)-7i⋅3-7i(-4i)(3+4i)(3-4i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 4 by 3.
12+4(-4i)-7i⋅3-7i(-4i)(3+4i)(3-4i)
Multiply -4 by 4.
12-16i-7i⋅3-7i(-4i)(3+4i)(3-4i)
Multiply 3 by -7.
12-16i-21i-7i(-4i)(3+4i)(3-4i)
Multiply -7i(-4i).
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Multiply -4 by -7.
12-16i-21i+28ii(3+4i)(3-4i)
Raise i to the power of 1.
12-16i-21i+28(i1i)(3+4i)(3-4i)
Raise i to the power of 1.
12-16i-21i+28(i1i1)(3+4i)(3-4i)
Use the power rule aman=am+n to combine exponents.
12-16i-21i+28i1+1(3+4i)(3-4i)
Add 1 and 1.
12-16i-21i+28i2(3+4i)(3-4i)
12-16i-21i+28i2(3+4i)(3-4i)
Rewrite i2 as -1.
12-16i-21i+28⋅-1(3+4i)(3-4i)
Multiply 28 by -1.
12-16i-21i-28(3+4i)(3-4i)
12-16i-21i-28(3+4i)(3-4i)
Subtract 28 from 12.
-16-16i-21i(3+4i)(3-4i)
Subtract 21i from -16i.
-16-37i(3+4i)(3-4i)
-16-37i(3+4i)(3-4i)
-16-37i(3+4i)(3-4i)
Simplify the denominator.
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Expand (3+4i)(3-4i) using the FOIL Method.
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Apply the distributive property.
-16-37i3(3-4i)+4i(3-4i)
Apply the distributive property.
-16-37i3⋅3+3(-4i)+4i(3-4i)
Apply the distributive property.
-16-37i3⋅3+3(-4i)+4i⋅3+4i(-4i)
-16-37i3⋅3+3(-4i)+4i⋅3+4i(-4i)
Simplify.
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Multiply 3 by 3.
-16-37i9+3(-4i)+4i⋅3+4i(-4i)
Multiply -4 by 3.
-16-37i9-12i+4i⋅3+4i(-4i)
Multiply 3 by 4.
-16-37i9-12i+12i+4i(-4i)
Multiply -4 by 4.
-16-37i9-12i+12i-16ii
Raise i to the power of 1.
-16-37i9-12i+12i-16(i1i)
Raise i to the power of 1.
-16-37i9-12i+12i-16(i1i1)
Use the power rule aman=am+n to combine exponents.
-16-37i9-12i+12i-16i1+1
Add 1 and 1.
-16-37i9-12i+12i-16i2
Add -12i and 12i.
-16-37i9+0-16i2
Add 9 and 0.
-16-37i9-16i2
-16-37i9-16i2
Simplify each term.
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Rewrite i2 as -1.
-16-37i9-16⋅-1
Multiply -16 by -1.
-16-37i9+16
-16-37i9+16
Add 9 and 16.
-16-37i25
-16-37i25
-16-37i25
Split the fraction -16-37i25 into two fractions.
-1625+-37i25
Simplify each term.
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Move the negative in front of the fraction.
-1625+-37i25
Move the negative in front of the fraction.
-1625-37i25
-1625-37i25
Rewrite in Standard Form (4-7i)/(3+4i)

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