Question

If x = a + bi and y = a - bi, solve x + 6y = 7 for x.

Answer 1

\[\large{a+bi + 6(a-bi)=7}\]
\[\large{a+bi+6(a)-6(bi)=7}\]
\[\large{a+6a+bi-6bi=7}\]

Answer 2

Can you try to add the like terms... ? @MSMR ?

Answer 3

We have
\[x=a+bi\]
and
\[y=a-bi\]
\[x+6y=7
\]
just plugin the value of x and y
\[(a+bi)+6(a-bi)=7\]
combine the like terms, what would you get @MSMR ?

Answer 4

@MSMR please interact ! others are trying to help you get to the answer thanks

Answer 5

I was trying it out, sorry

Answer 6

No problem MSMR take your time...

Answer 7

But just reply so that we can believe that you r trying

Answer 8

so if you combine like terms and get 7a = 5bi = 7, I'm a lil confused on what to do next.

Answer 9

\[\large{7a-5bi=7}\]

Answer 10

did u mean this?

Answer 11

right

Answer 12

but then how do you solve for x, since it's not even in the equation anymore? do you put it in a + bi form and divide out (if that makes sense?)

Answer 13

wait

Answer 14

@MSMR let me knw if you need an alternate soln

Answer 15

do you have options?

Answer 16

that might be helpful because i'm not sure what to do once I've combined like terms

Answer 17

no, that's the whole problem and I don't have the answers.

Answer 18

ok... \[\large{x+6y=7}\]
\[\large{x=7-6y}\]
\[\large{x=7-6(a-bi)}\]
\[\large{x=7-6a+6bi}\]

Answer 19

wht u think @AravindG and @ash2326

Answer 20

@MSMR a complex no. is of the form a+bi
a= real part
b= imaginary part
we got
\[7a-5bi=7\]
or we have
\[7a-5bi=7+0i\]
now compare both sides
equating real part
\[7a=7\]
\[-5b=0\]
can you find a and b now?

Answer 21

*equating complex parts
\[-5b=0\]

Answer 22

so is a=7 and b=0?

Answer 23

Yes, you're right

Answer 24

so would x = 7? (7 + 0)

Answer 25

yeah :)

Answer 26

@MSMR do you get this?

Answer 27

I think so, yeah. I'll try to do the rest of my homework and see. Thank you (all of you!)

Answer 28

good:D
you're welcome :)