Question

Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part?

A. 2 + 3i

B. 2 − 3i

C. 3i + 2

D. 3i − 2

Answer 1

It depends.

Answer 2

you didn't say what it is, are you looking for a conjugate of \[\huge\color{blue}{ 2+3i~~~~~~~~~~~~or~~~~~~~~~~2-3i } \]

Answer 3

I will assume that the first option I wrote is correct, because when someone says 3i, they mean +3i, not -3i.

the conjugate for \[\huge\color{blue}{ a+bi } \]
where a and b are CONSTANTS is \[\huge\color{red}{ a-bi } \]

Answer 4

The reason for this, is so that an imaginary number (which is also considered to be a RADICAL ) on the bottom would cancel.
\[For~~~example:~~~\color{black}{ \frac{4}{2+3i} } \]\[\frac{4}{2+3i} \color{red}{ \times \frac{2-3i}{2-3i} } \]\[\frac{4(2-3i)}{(2+3i)(2-3i)} \] \[(a-b)(a+b)=a^2-b^2\] \[\color{black}{ \frac{4(2-3i)}{2^2-(3i)^2} } \]\[\color{black}{ \frac{4(2-3i)}{4-(-9)} } \]\[\color{black}{ \frac{4(2-3i)}{13} } \]\[\color{black}{ \frac{8-12i}{13} } \]

Answer 5

that's the purpose of conjugate, REMOVE the radical from the denominator.

Answer 6

@SolomonZelman everything you sent, was sent to me in symbols that i can read on my computer. any other way you can show me? "frac{4(2-3i)}{4-(-9)} } \]\[\color{black}{ \frac{4(2-3i)}{13} } \]\[\color{black}{ \frac{8-12i}{13} } \]"

Answer 7

Damn it!!! I thought only the drawing tool doesn't work; AND THE EQUATION EDITOR?!?!?!

Answer 8

@SolomonZelman :( sorry!!!! but at least on my computer, i cant see it :/

Answer 9

I didn't do your problem, I just showed a different example.