May 5th, 2011, 09:32 PM  #1 
Senior Member Joined: Dec 2010 Posts: 233 Thanks: 0  Complex number
1. Determine the value of m if z= ?5+mi/42?5i is a pure complex number and find this real number. 2. Express (1+i)^3/(1i)^5 in the form a+ib, where a and b are real. Hence, find the argument and modulus of this complex number. I need help. I can't even solve one of the question. It is an exam question. Please show me step by step how you solving the question. Thank you. 
May 5th, 2011, 09:46 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Complex number
1.) What is a pure complex number? 2.) One way to do this is through use of Euler's formula: Now you should be able to easily compute the argument and modulus. 
May 5th, 2011, 09:55 PM  #3 
Senior Member Joined: Jun 2010 Posts: 618 Thanks: 0  Re: Complex number
MarkFL, I think by 'pure complex' is meant the same as 'pure imaginary', i.e. it lies on the imaginary axis. Ormkärr 
May 5th, 2011, 10:08 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Complex number
I thought that was probably the case, but I wasn't sure...thanks! In that case, it appears we should set: I don't know what you mean by "find this real number" because z and m are imaginary. 
May 5th, 2011, 10:30 PM  #5 
Senior Member Joined: Jun 2010 Posts: 618 Thanks: 0  Re: Complex number
MarkFL, You are being deceived by the poor typesetting employed in the OP. I am convinced it should read In this case, I think the answer is real. Ormkärr 
May 5th, 2011, 10:39 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Complex number
Aw jeeez! This isn't the first time such a thing has happened! I'm so entrenched in the use of parentheses for clarity, I tend to assume everyone else is too. 
May 5th, 2011, 10:44 PM  #7 
Senior Member Joined: Jun 2010 Posts: 618 Thanks: 0  Re: Complex number
It's probably better for your health to give the benefit of the doubt as you do! I for one should be scoping out good deals on cemetery plots, given my level of faith in my fellow man. Ormkärr 
May 6th, 2011, 03:22 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 18,037 Thanks: 1394 
2. 
May 6th, 2011, 07:44 AM  #9 
Senior Member Joined: Dec 2010 Posts: 233 Thanks: 0  Re: Complex number
I still don't understand question 1.

May 6th, 2011, 07:55 AM  #10 
Senior Member Joined: Jun 2010 Posts: 618 Thanks: 0  Re: Complex number
hoyy1kolko, If we write then we want to "realize" (my version of "rationalize", not standard) the denominator, so multiply top and bottom by the complex conjugate of the denominator, namely 4+2?5i to get At this point, since you want a 'pure imaginary' number, you must have the real part of the above vanish, so you set and you are done. Ormkärr 

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