Rationalizing complex numbers when the denominator has a (+ 1) added to it
up vote
0
down vote
favorite
If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
asked Nov 21 at 10:45
ming
282
add a comment |
up vote
0
down vote
favorite
If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
asked Nov 21 at 10:45
ming
282
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
asked Nov 21 at 10:45
ming
282
If I were to try and rationalize a complex number like $Z + 2W + 3 over Z + 1$, when I multiply by the conjugate of Z to make the denominator a real number, do I have to write z(conjugate)/z(conjugate) or z(conjugate) + 1/z(conjugate) + 1 or z(conjugate) - 1/z(conjugate) - 1??
(I'm sorry idk how to format the conjugate can someone help edit)
complex-numbers
complex-numbers
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
asked Nov 21 at 10:45
ming
282
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
asked Nov 21 at 10:45
ming
282
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
edited Nov 21 at 10:50
José Carlos Santos
141k19111207
141k19111207
asked Nov 21 at 10:45
ming
282
asked Nov 21 at 10:45
ming
282
asked Nov 21 at 10:45
ming
282
282
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
add a comment |
up vote
1
down vote
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
add a comment |
up vote
1
down vote
up vote
1
down vote
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
If $Z,Winmathbb{C}$ (and $Zneq-1$) and if you wish to express $dfrac{Z+2W+3}{Z+1}$ has a quotient whose denominator is a real number, the natural option consists in multiplying both numerator and denominator with $overline{Z+1}$, thereby getting$$frac{Z+2W+3}{Z+1}=frac{(Z+2W+3)left(overline{Z+1}right)}{(Z+1)left(overline{Z+1}right)}=frac{(Z+2W+3)left(overline Z+1right)}{lvert Z+1rvert^2}.$$
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
answered Nov 21 at 10:50
José Carlos Santos
141k19111207
141k19111207
add a comment |
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3007554%2frationalizing-complex-numbers-when-the-denominator-has-a-1-added-to-it%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
