## Signs in the complex number: (3 + 5i)/(6i)

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
honest_denverco09
Posts: 42
Joined: Tue Mar 31, 2009 2:06 am
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### Signs in the complex number: (3 + 5i)/(6i)

I am rewriting this quotient into the form (a + bi), but i am stuck in the signs of the imaginary and the real number parts.

I have : (3 + 5i)/(6i)
I did multiply this fraction by (6i) for both of Numerator and Denominator. As a result, i had ( (-1/2)i + 5/6 ).
But computer's answer is opposite to my answer 's signs. He got ( (1/2)i - 5/6 ).

I would like to ask where are my mistakes ?

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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### Re: Signs in the complex number

I am rewriting this quotient into the form (a + bi), but i am stuck in the signs of the imaginary and the real number parts.

I have : (3 + 5i)/(6i)
I did multiply this fraction by (6i) for both of Numerator and Denominator. As a result, i had ( (-1/2)i + 5/6 ).
But computer's answer is opposite to my answer 's signs. He got ( (1/2)i - 5/6 ).

I would like to ask where are my mistakes ?
I get what you get

$\frac{3+5i}{6i}=\frac{3+5i}{6i}\cdot\frac{6i}{6i}=\frac{18i+30i^2}{36i^2}=\frac{18i+30(-1)}{36(-1)}=\frac{18i}{-36}+\frac{-30}{-36}=-\frac{1}{2}i+\frac{5}{6}$

though I would have just multiplied by $\frac{i}{i}$

honest_denverco09
Posts: 42
Joined: Tue Mar 31, 2009 2:06 am
Contact:

Thanks!