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#1 2007-02-16 16:58:08

Registered: 2005-06-28
Posts: 22,081

Complex Numbers Ex.1


Exercise 1

1. What is the conjugate of 1/(1+i)?

2. Find the real and imaginary parts of the Complex number 1/(5+4i).

3. Find the modulus of (3-i)(2+i)/(2-i).

4. If x+iy=3/(2+Cosθ+iSinθ), prove that x²+y² = 4x-3.

5. What is the argument of the complex number -1+i?

6. Find the modulus and argument of the complex number -√6-√2i.

7. If (a+ib) (c+id) = (p+iq), prove that (a²+b²) (c²+d²) = (p²+q²).

8. Express the complex number 2+2√3i in the polar form (that is, in the form aCosθ + ibSinθ.

9. Prove that the points 3+7i, 6+5i, and 15-i are collinear in the Argand plane.

10. Prove that the points representing the complex numbers -1, 3+i, 2+2i, and -2+i on the Argand plane are the vertices of a parallelogram.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.


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