I'm totally with you .. but once you've multiplied by i you've changed the cosmetics of the number .. isn't it matter? I mean isn't it matter for changing the definition of the number itself? who said that multiplying isn't changing the typecast of the number itself? really weird ..The form:
[MATH]a+bi[/MATH]
is referred to as the rectangular form for a complex number, which is just one of many forms in which complex numbers may be written. It is a particularly useful form though. Also, observe:
[MATH]\frac{1}{2i}=\frac{1}{2i}\cdot\frac{i}{i}=\frac{i}{2i^2}=-\frac{i}{2}=0+\left(-\frac{1}{2}\right)i[/MATH]
no didn't been asked, while solving a question I was encountered to convert that horrible number of complex to a+biI would guess [you] have been asked to write this number in the rectangular form:
[MATH]a+bi[/MATH]
\(\displaystyle \begin{align*}\dfrac{3-4\mathcal{i}}{7+5\mathcal{i}}&=\dfrac{(3-4\mathcal{i})(7-5\mathcal{i})}{49+25} \\&=\dfrac{(21-20)+\mathcal{i}(-15-28)}{74}\\&=\dfrac{1}{74}+\bigg( \dfrac{-43}{74} \bigg) \mathcal{i}\end{align*}\)lets assume I have complex number like (3-4i / 5j +7 ) then it's right to write like this :
(3-4i / 5j +7 ) = a + b*i
[MATH]0+\left(-\frac{1}{2}\right)i[/MATH]
I would have called this a typo except that it has been carried through on a couple occasions.(3-4i / 5j +7 ) = a + b*i
Yes, in general, it's common to express the addition of a negative number as subtraction of its opposite. In particular, it's also common for authors who want to explicitly match the given form a+bi to stick with addition when b is negative by putting grouping symbols around it (like in posts #2 and #10).It is common to write … \(\displaystyle 0 - \tfrac{1}{2}i\)
… it is common to write … \(\displaystyle \tfrac{1}{74} - \tfrac{43}{74}i\)
It is common to write this final result in "a + bi" form as \(\displaystyle \ 0 - \tfrac{1}{2}i\).
Regarding post #10:
Likewise, it is common to write this final result in "a + bi" form as \(\displaystyle \ \tfrac{1}{74} - \tfrac{43}{74}i\).
Correct & thank you.For the sake of the OP, I wanted to give the number strictly in the form: [MATH]a+bi[/MATH]
That top right denominator should be "49 + 25."
Likewise, it is common to write this final result in "a + bi" form as \(\displaystyle \ \tfrac{1}{74} - \tfrac{43}{74}i\).
For the sake of the OP, I wanted to give the number strictly in the form:
[MATH]a+bi[/MATH]
Correct & thank you.
I have never figured why some want-to-bes must correct every little thing.
But in this case the "correction" is a mistake. It does say a real number \(\displaystyle a\) plus a real number \(\displaystyle b\) times \(\displaystyle \mathcal{i}\).
To Lookagain, where did I say anything about you? I did not. Did I? Can you point to anything that I posted which namers you?pka, this is the second post of yours that has been reported in recent weeks for you attacking me with your insults. You need to stop posting until you can be civil.