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00:00 - 00:59 | photo.net today we are going to discuss a problem on complex number that is what is the smallest positive integer of N for which one plus I power to INR is equal to 1 minus power to so what they are asking as is to find out the smallest integer in which satisfies the given equation aapke latest find this problem solution sofa given that even that 1 + I2 n is equal to 1 minus I power to in ok so letters write this one oneplus I squared more power in is equal to 1 minus y |

01:00 - 01:59 | square Mall power ok understood so this one is nothing but one plus I ho school so what I am going to write is 1 + 2 Y + Y square whole power in is equal to 1 minus 2 Y + y whole square whole power in this will result into 1 minus 1 + 2 whole power in is equal to 1 minus 1 minus 2 Y all power in 10 - 1 + 1 get Kansas we will be left with 2 into power -2 this can be written as to power in eye power in this can be written as - 1 power in eye power |

02:00 - 02:59 | 2 power n to power and to power when will get cancelled my power n is equal to minus one power in into power in if fire fire in is equal to 1 is equal to minus y this is not satisfied not satisfied b n is equal to 2 I squared is equal to -1 square square that is -1 -1 square will be plus one this is also one satisfied so letters to father also for 10 years 1 v |

03:00 - 03:59 | 3i cube minus 1 whole cube IQ this will be minus is equal to minus of -5 which is place I since I cube is equal to minus minus y + Y is not same right so therefore it does not satisfy not satisfied therefore we can come for a conclusion that the smallest the smallest integer for which the given equation satisfies for which the given equation satisfies fattest voice is too so that is in is equal to 2 |

04:00 - 04:59 | and the equation will be satisfied by multiples of 2 and they are the smallest numbers so we wish to thank you |

**Why we need Complex Number ?**

**Algorithm to find integral exponents of iota and generalize in terms of 4n+1 ; 4n; 4n+2**

**Definition Of Complex Numbers**

**Equality of complex numbers**

**Addition of complex number and their properties**

**Subtraction of complex numbers**

**multiplication of two complex no. and their properties**

**Division of two complex number**

**Conjugate of a complex no and its properties. If `z, z_1, z_2` are complex no.; then :-
(i) `bar(barz)=z` (ii)`z+barz=2Re(z)`(iii)`z-barz=2i Im(z)` (iv)`z=barz hArr z` is purely real (v) `z+barz=0implies` z is purely imaginary (vi)`zbarz=[Re(z)]^2+[Im(z)]^2`**

**Properties of a complex no. If `z;z_1;z_2` are complex no.; then (vii)`bar(z_1+z_2)=barz_2+barz_1` (viii)`bar(z_1-z_2)=barz_1-barz_2` (ix)`bar(z_1z_2)=barz_1barz_2` (x) `(barz_1)/z_2=barz_1/barz_2` where `z_2!=0`**