Home
Class 11
MATHS
Evaluate : [i^(18)+(1/i)^(25)]^3...

Evaluate : `[i^(18)+(1/i)^(25)]^3`

Text Solution

Verified by Experts

The correct Answer is:
N/a
`[ i^(18)+((1)/(i))^(25)] ^(3)=[i^(( 4xx4)+2)+(1)/(i^(25))]^(3)`
`=[i^(4xx4)*i^(2)+(1)/(i^(4xx6)*i)]^(3)=[1*i^(2)+(1)/(1*i)]^(3)`
`=[i^(2)+(i)/(i^(2))]^(3)=[-1-i]^(3)=[-(1+i)]^(3) `
`=[i^(2)+(i)/(i^(2))]^(3)=[-1-i^(3)] =[-(1+i)]^(3)`
`=-(1+i)^(3)=- [1^(3)+i^(3) + 3*1*i(1+ i)] `
`=-[1-i+3i+3i^(2)] =-[1+2i-3]`
` = - [-2+2i]=2-2i`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE 5.3|10 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exericse|20 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|8 Videos

Similar Questions

Explore conceptually related problems

Evaluate: [i^19+(1/i)^25]^2

Evaluate : (i) 1-:(1)/(3)

Simplify: [i^(18) + ((1)/(i))^(25)]^(3)

Evaluate : (i) i^(135) (ii) i^(-47) (iii) (-sqrt(-1))^(4n +3) , n in N (iv) sqrt(-25) + 3sqrt(-4) + 2 sqrt(-9)

Evaluate. (i) i^(1998) (ii) i^(-9999) (iii) (-sqrt-1)^(4n=3) ,n ne N

Simplify the following : (i) [i^(19) +(1)/(i^(25))]^(2) (ii) [i^(5)- (1)/(i^(3))]^(4)

Show that: {i^(19)+(1/i)^(25)}^2=-4 (ii) {i^(17)-(1/i)^(34)}^2=2i (iii) {i^(18)+(1/i)^(24)}^3=0 (iv) i^n+i^(n+1)+i^(n+2)+i^(n+3)=0 for all n in Ndot

Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

Evaluate: (i^2+i^4+i^6+i^7)/(1+i^2+i^3)

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

Home
Profile