IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: loggerhead on October 23, 2009, 01:13:25 am

Title: Complex numbers Question A2 maths
Post by: loggerhead on October 23, 2009, 01:13:25 am

please help me with this question

The complex number u is given by
u = 7 + 4i
      3 - 2i

(i) Express u in the form x + iy, where x and y are real.              [3]

(ii) Sketch an Argand diagram showing the point representing the complex number u. Show on the same diagram the locus of the complex number z such that |z - u|= 2.            [3]

(iii) Find the greatest value of arg z for points on this locus.

i can do (i) and (ii) no problem but i need help with part 3 please

this is question 7 from CIE Maths paper 3 Oct/Nov 2003 which is attached

Title: Re: Complex numbers Question A2 maths
Post by: sameer210394 on October 23, 2009, 06:33:47 am

Quote from: loggerhead on October 23, 2009, 01:13:25 am

please help me with this question

The complex number u is given by
u = 7 + 4i
      3 - 2i

(i) Express u in the form x + iy, where x and y are real.              [3]

(ii) Sketch an Argand diagram showing the point representing the complex number u. Show on the same diagram the locus of the complex number z such that |z - u|= 2.            [3]

(iii) Find the greatest value of arg z for points on this locus.

i can do (i) and (ii) no problem but i need help with part 3 please

this is question 7 from CIE Maths paper 3 Oct/Nov 2003 which is attached

i'm gettin the answer for (iii) as 2.2 radians... just check,,, i donno if its right...

Title: Re: Complex numbers Question A2 maths
Post by: astarmathsandphysics on October 23, 2009, 08:08:04 am

Arg u + arcsin (2/|u|)

Title: Re: Complex numbers Question A2 maths
Post by: loggerhead on October 24, 2009, 09:04:18 pm

o yea, so simple.

thank you