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

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

Text Solution

AI Generated Solution

To evaluate the expression \([i^{18} + (1/i)^{25}]^3\), we will follow a step-by-step approach. ### Step 1: Simplify \(i^{18}\) We know that the powers of \(i\) (where \(i = \sqrt{-1}\)) repeat every 4 terms: - \(i^1 = i\) - \(i^2 = -1\) - \(i^3 = -i\) - \(i^4 = 1\) ...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|17 Videos

  • CONIC SECTIONS

    NCERT ENGLISH|Exercise EXERCISE 11.1|15 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