complex no. help (1 Viewer)

[totallybord]

hi!
help me with my complex no.s plz
1) how do you convert (2-2√3i)^-4 to mod-arg form? is there a really easy way?

2) if the mod-arg form is in degrees eg. cis35 is that still calld mod-arg?

3) how do i no that z^6 +1 = (z^2+1) (z^4+z^2+1) i havnet done polynomials...is there some kind of rule or is it common sense

4) i dun get why if |z1| =|z2| not equal to 0, why is arg (z2-z1/z2+z1) = plus or minus pi/2? what the hell is it talking abt? what does the putting z2-z1 over z2+z1mean anyway?

5) what are real quadratic factors and what are comples linear factors ?

6)prove that for any 2 complex no.s z1 and z2
|z1+z2|>or equal to |z1|-|z2| assuming |z1>|z2|...when does the equality sing hold? i no this is the whole triangular inequality thingy, bt how do i prove it and write the working out for it?

thanks!

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[Mark576]

3) z⁶ + 1 = (z²)³ + 1³

Now using the identity for sum of cubes:

z⁶ + 1 = (z² + 1)(z⁴ + z² + 1)

 

[solomarc20]

1) Convert the complex number into mod-arg form. (Draw a right angled triangle on an Argand diagram. Get the modulus using Pythagoras and the Argument using Trigonometry. It is a lot easier 2 do if u've got a diagram) Then use DeMoivre's theorem... and simplify

2)Always have the answer in Radians, since the principal argument is defined in terms of Radians...