Rewrite in Standard Form (4+i)/(8i)

Math
4+i8i
Multiply the numerator and denominator of 4+i8i by the conjugate of 8i to make the denominator real.
4+i8i⋅ii
Multiply.
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Combine.
(4+i)i8ii
Simplify the numerator.
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Apply the distributive property.
4i+ii8ii
Multiply ii.
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Raise i to the power of 1.
4i+i1i8ii
Raise i to the power of 1.
4i+i1i18ii
Use the power rule aman=am+n to combine exponents.
4i+i1+18ii
Add 1 and 1.
4i+i28ii
4i+i28ii
Rewrite i2 as -1.
4i-18ii
Reorder 4i and -1.
-1+4i8ii
-1+4i8ii
Simplify the denominator.
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Add parentheses.
-1+4i8(ii)
Raise i to the power of 1.
-1+4i8(i1i)
Raise i to the power of 1.
-1+4i8(i1i1)
Use the power rule aman=am+n to combine exponents.
-1+4i8i1+1
Add 1 and 1.
-1+4i8i2
Rewrite i2 as -1.
-1+4i8⋅-1
-1+4i8⋅-1
-1+4i8⋅-1
Multiply 8 by -1.
-1+4i-8
Split the fraction -1+4i-8 into two fractions.
-1-8+4i-8
Simplify each term.
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Dividing two negative values results in a positive value.
18+4i-8
Cancel the common factor of 4 and -8.
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Factor 4 out of 4i.
18+4(i)-8
Cancel the common factors.
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Factor 4 out of -8.
18+4i4⋅-2
Cancel the common factor.
18+4i4⋅-2
Rewrite the expression.
18+i-2
18+i-2
18+i-2
Move the negative in front of the fraction.
18-i2
18-i2
Rewrite in Standard Form (4+i)/(8i)

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