# complex numbers

in an argand diagram the points a and b represent 1+7i and 4+3i respectively and o is the origin the quadrilateral oabc is a parallelogra find the complex numbler represented by point c
i set the gradients equal but that gives just one equation 4x+3y=0 same thing with the distances just one equation and dont know how to move from there
can i use the simple gradient method to this question or do i have to use another method to solve. this?

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Original post by mikeft
in an argand diagram the points a and b represent 1+7i and 4+3i respectively and o is the origin the quadrilateral oabc is a parallelogra find the complex numbler represented by point c
i set the gradients equal but that gives just one equation 4x+3y=0 same thing with the distances just one equation and dont know how to move from there
can i use the simple gradient method to this question or do i have to use another method to solve. this?

A quick sketch of the points and the parallelogram should convince you its a very simple answer?
Original post by mqb2766
A quick sketch of the points and the parallelogram should convince you its a very simple answer?

not really ive done a sketch
Original post by mikeft
not really ive done a sketch

Original post by mqb2766

sure its just a parallelogram with the points though nothing much to it so could you explain the solution to the question please
(edited 1 year ago)
Original post by mikeft
sure its just a parallelogram with the points though nothing much to it so could you explain the solution to the question please

If you followed the path from O to C by following A first, what is the line segment AC equal to?
Original post by mqb2766
If you followed the path from O to C by following A first, what is the line segment AC equal to?

3y+4x=0 i am not sure what the path from o to c by following a first means though
Original post by mikeft
3y+4x=0 i am not sure what the path from o to c by following a first means though

Can you upload what you sketched pls.
Youre sort of thinking about it ~correctly, but its much simpler than you imagine.
(edited 1 year ago)
Original post by mqb2766
Can you upload what you sketched pls.
Youre sort of thinking about it ~correctly, but its much simpler than you imagine.

yes i can okay. but what do i do next?
What is the complex number represented by the line segment AB? That must correspond to OC?
3y+4x-25=0
Original post by mikeft
3y+4x-25=0

Im not sure how youre getting this,
OB = OA + AB
You know OA and OB so AB = ... = OC
Original post by mqb2766
Im not sure how youre getting this,
OB = OA + AB
You know OA and OB so AB = ... = OC

why does ob=oa+ab?
Original post by mikeft
why does ob=oa+ab?

That is how you add vectors or complex numbers, tip to tail.
Your textbook must have an example?
Original post by mqb2766
That is how you add vectors or complex numbers, tip to tail.
Your textbook must have an example?

i dont think so we dont use vectors is there another way to do. this without them?
Original post by mikeft
i dont think so we dont use vectors is there another way to do. this without them?

Is how you add complex numbers.
Original post by mqb2766
Is how you add complex numbers.

um well i havent seen that before is there another more simple way or could you explain this
Original post by mikeft
um well i havent seen that before is there another more simple way or could you explain this

If youre doing a question about the mod/arg of complex numbers, you must have covered adding them?
From your diagram, changes in x and changes in y's should do it.
(edited 1 year ago)
Original post by mqb2766
If youre doing a question about the mod/arg of complex numbers, you must have covered adding them?

yes i think i figured that part know, but about ob=oa+oc doesnt that mean modulus b=modulusa+modulusc but that gives an answer with roots not the 3-4i that i am looking for