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chimanshu_007

Heyyy

well some more help frm my side for my dear goiitians

HOPE IT WILL HELP U ALL....

1St of all.....to find square root

z = a + ib

its sq root =

+- [( (| Z | + a )/ 2) + i (( | Z | - a) / 2)]...(if b > 0)

if b < 0

then its -ive sign before i

2) | z - z₁|/ |z - z₂| = k

then locus is a circle if k =/= 1

and its a straight line if k = 1

3)|z - z₁| - |z - z₂| = 2a , then locus =

(i) ellipse , if 2a > |z₁ - z₂|

(ii) hyperbola , if 2a < |z₁ - z₂|

4)in qs like..

|z - z₁| + |z - z₂| = constant

and coeff of z on both mods is 1 then for sure its locus is an ellipse

and if coeff are different , then it will be parabola for sure

5)z₁ and z_{2 are 2 complex no.s such that}

|z₁ + z₂| = | z₁| + |z₂|

progressions

if given a_n = 2n + 1....and given its an AP...

then the common diff = coeff of n

i.e 2 here

a_n = 5n + 1 , then C.D = 5

7) in case sum is given , An² + B

then common diff = 2 (coeff of n²)

i.e 2A

8) in case of AM inserted

a , A1 , A2.....An , b

common diff d = b - a / n + 1

n = no. of inserted terms...

THESE ARE SOME OF THE SHRTCTS....

MORE ARE COMING SOON

hope these all help....plzz cpmment if u like it....