Rewrite in Standard Form (9i)/(3-7i)

Math
9i3-7i
Multiply the numerator and denominator of 9i3-7i by the conjugate of 3-7i to make the denominator real.
9i3-7i⋅3+7i3+7i
Multiply.
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Combine.
9i(3+7i)(3-7i)(3+7i)
Simplify the numerator.
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Apply the distributive property.
9i⋅3+9i(7i)(3-7i)(3+7i)
Multiply 3 by 9.
27i+9i(7i)(3-7i)(3+7i)
Multiply 9i(7i).
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Multiply 7 by 9.
27i+63ii(3-7i)(3+7i)
Raise i to the power of 1.
27i+63(i1i)(3-7i)(3+7i)
Raise i to the power of 1.
27i+63(i1i1)(3-7i)(3+7i)
Use the power rule aman=am+n to combine exponents.
27i+63i1+1(3-7i)(3+7i)
Add 1 and 1.
27i+63i2(3-7i)(3+7i)
27i+63i2(3-7i)(3+7i)
Simplify each term.
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Rewrite i2 as -1.
27i+63⋅-1(3-7i)(3+7i)
Multiply 63 by -1.
27i-63(3-7i)(3+7i)
27i-63(3-7i)(3+7i)
Reorder 27i and -63.
-63+27i(3-7i)(3+7i)
-63+27i(3-7i)(3+7i)
Simplify the denominator.
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Expand (3-7i)(3+7i) using the FOIL Method.
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Apply the distributive property.
-63+27i3(3+7i)-7i(3+7i)
Apply the distributive property.
-63+27i3⋅3+3(7i)-7i(3+7i)
Apply the distributive property.
-63+27i3⋅3+3(7i)-7i⋅3-7i(7i)
-63+27i3⋅3+3(7i)-7i⋅3-7i(7i)
Simplify.
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Multiply 3 by 3.
-63+27i9+3(7i)-7i⋅3-7i(7i)
Multiply 7 by 3.
-63+27i9+21i-7i⋅3-7i(7i)
Multiply 3 by -7.
-63+27i9+21i-21i-7i(7i)
Multiply 7 by -7.
-63+27i9+21i-21i-49ii
Raise i to the power of 1.
-63+27i9+21i-21i-49(i1i)
Raise i to the power of 1.
-63+27i9+21i-21i-49(i1i1)
Use the power rule aman=am+n to combine exponents.
-63+27i9+21i-21i-49i1+1
Add 1 and 1.
-63+27i9+21i-21i-49i2
Subtract 21i from 21i.
-63+27i9+0-49i2
Add 9 and 0.
-63+27i9-49i2
-63+27i9-49i2
Simplify each term.
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Rewrite i2 as -1.
-63+27i9-49⋅-1
Multiply -49 by -1.
-63+27i9+49
-63+27i9+49
Add 9 and 49.
-63+27i58
-63+27i58
-63+27i58
Split the fraction -63+27i58 into two fractions.
-6358+27i58
Move the negative in front of the fraction.
-6358+27i58
Rewrite in Standard Form (9i)/(3-7i)

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