Rewrite in Standard Form (-2+2i)/(3-8i)

Math
-2+2i3-8i
Multiply the numerator and denominator of -2+2i3-8i by the conjugate of 3-8i to make the denominator real.
-2+2i3-8i⋅3+8i3+8i
Multiply.
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Combine.
(-2+2i)(3+8i)(3-8i)(3+8i)
Simplify the numerator.
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Expand (-2+2i)(3+8i) using the FOIL Method.
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Apply the distributive property.
-2(3+8i)+2i(3+8i)(3-8i)(3+8i)
Apply the distributive property.
-2⋅3-2(8i)+2i(3+8i)(3-8i)(3+8i)
Apply the distributive property.
-2⋅3-2(8i)+2i⋅3+2i(8i)(3-8i)(3+8i)
-2⋅3-2(8i)+2i⋅3+2i(8i)(3-8i)(3+8i)
Simplify and combine like terms.
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Simplify each term.
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Multiply -2 by 3.
-6-2(8i)+2i⋅3+2i(8i)(3-8i)(3+8i)
Multiply 8 by -2.
-6-16i+2i⋅3+2i(8i)(3-8i)(3+8i)
Multiply 3 by 2.
-6-16i+6i+2i(8i)(3-8i)(3+8i)
Multiply 2i(8i).
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Multiply 8 by 2.
-6-16i+6i+16ii(3-8i)(3+8i)
Raise i to the power of 1.
-6-16i+6i+16(i1i)(3-8i)(3+8i)
Raise i to the power of 1.
-6-16i+6i+16(i1i1)(3-8i)(3+8i)
Use the power rule aman=am+n to combine exponents.
-6-16i+6i+16i1+1(3-8i)(3+8i)
Add 1 and 1.
-6-16i+6i+16i2(3-8i)(3+8i)
-6-16i+6i+16i2(3-8i)(3+8i)
Rewrite i2 as -1.
-6-16i+6i+16⋅-1(3-8i)(3+8i)
Multiply 16 by -1.
-6-16i+6i-16(3-8i)(3+8i)
-6-16i+6i-16(3-8i)(3+8i)
Subtract 16 from -6.
-22-16i+6i(3-8i)(3+8i)
Add -16i and 6i.
-22-10i(3-8i)(3+8i)
-22-10i(3-8i)(3+8i)
-22-10i(3-8i)(3+8i)
Simplify the denominator.
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Expand (3-8i)(3+8i) using the FOIL Method.
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Apply the distributive property.
-22-10i3(3+8i)-8i(3+8i)
Apply the distributive property.
-22-10i3⋅3+3(8i)-8i(3+8i)
Apply the distributive property.
-22-10i3⋅3+3(8i)-8i⋅3-8i(8i)
-22-10i3⋅3+3(8i)-8i⋅3-8i(8i)
Simplify.
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Multiply 3 by 3.
-22-10i9+3(8i)-8i⋅3-8i(8i)
Multiply 8 by 3.
-22-10i9+24i-8i⋅3-8i(8i)
Multiply 3 by -8.
-22-10i9+24i-24i-8i(8i)
Multiply 8 by -8.
-22-10i9+24i-24i-64ii
Raise i to the power of 1.
-22-10i9+24i-24i-64(i1i)
Raise i to the power of 1.
-22-10i9+24i-24i-64(i1i1)
Use the power rule aman=am+n to combine exponents.
-22-10i9+24i-24i-64i1+1
Add 1 and 1.
-22-10i9+24i-24i-64i2
Subtract 24i from 24i.
-22-10i9+0-64i2
Add 9 and 0.
-22-10i9-64i2
-22-10i9-64i2
Simplify each term.
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Rewrite i2 as -1.
-22-10i9-64⋅-1
Multiply -64 by -1.
-22-10i9+64
-22-10i9+64
Add 9 and 64.
-22-10i73
-22-10i73
-22-10i73
Split the fraction -22-10i73 into two fractions.
-2273+-10i73
Simplify each term.
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Move the negative in front of the fraction.
-2273+-10i73
Move the negative in front of the fraction.
-2273-10i73
-2273-10i73
Rewrite in Standard Form (-2+2i)/(3-8i)

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