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Calculus/Complex numbers

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Expert: - 5/4/2008


Question

Complex Number
please see the image attached. I am studying A Level Maths. Thanks for your time and help.

Answer
Questioner:   jenny
Category:  Calculus
Private:  No
 
Subject:  complex numbers
Question:  
.......................
Hi, again, Jenny,

(see earlier comments)  

If you have more than one question, put them together.  If you send several questions, you use up my quota, which is unfair to other questioners.

......................................
Your equation was;  

(1 - i) z -  2i zbar = -2 + 3i

which means:

(1 - i)(x + iy) -  2i(x - iy) = -2 + 3i

Now mutliply that out,

x + iy - ix - i^2y -  2ix + 2i^2y = -2 + 3i

Remember that  i^2 = -1:

x + iy - ix + y -  2ix - 2y = -2 + 3i

Now separate and equate real parts and imaginary parts:

x + y  - 2y  + iy - ix - 2ix = -2 + 3i

x + y - 2y  + (y - x - 2x)i = -2 + 3i

x  - y  + (y - 3x)i = -2 + 3i

 x - y = - 2
-3x + y =  3

Solve your two simultaneous equations now.  I'll leave that to you.

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

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