Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2008-12-28 03:02:52

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,222

Complex Numbers - Pre-University level - II

1. Find the modulus or the absolute value of

.

2. Find the modulus and argument of the following complex numbers:-
(1)


(2)

(3)
.

3. Prove that the complex numbers


are the vertices of an equilateral triangle in the complex plane.

4. Prove that the points representing the complex numbers 2i, 1+i, 4+4i, and 3+5i on the Argand plane are the vertices of a rectangle.

5. Find the square root of (-7+24i).

6. If (1+i)(1+2i)(1+3i)......(1+ni) = x+iy, show that
2.5.10.......(1+n²) = x² + y²

7. Express the following complex numbers in polar form.
(1) 2 + 2√3
(2) -1 + i√3

8. Prove that |z| =1 if

.

9. P represents the variable complex number z, find the locus of P if
(i)


(ii)
.

10. If one of the roots is 2+√3 i, solve the equation

.


Character is who you are when no one is looking.

Offline

Board footer

Powered by FluxBB