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#1 2007-02-17 15:58:08

ganesh
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Complex Numbers Ex.1

COMPLEX NUMBERS

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 x+y = 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 (a+b) (c+d) = (p+q).

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.


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