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

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

A

`2i`

B

`3-2i`

C

`2-2i`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
`[ 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`
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NAGEEN PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATION -MISCELLANEOUS EXERCISE
  1. Evaluate : [i^(18)+(1/i)^(25)]^3

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  2. Prove that Re (z1 z2)= Re z1 Re z2 - Imz1 Imz2 ,

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  3. Reduce (1/(1-4i)-2/(1+i))((3-4i)/(5+i))to the standard form.

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  4. If (a+i b)/(c+i d)=x+i y , prove that (a-i b)/(c-i d)=x-i ya n d(a^2+b...

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  5. Convert the following in the polar form : (i) (1+7i)/((2-i)^2) (ii) (...

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  6. Solve the equation : 3x^2-4x+(20)/3=0

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  7. x^(2)-2x+(3)/(2)=0

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  8. Solve the equation :27 x^2-10 x+1=0

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  9. Solve the following quadratic: 21 x^2-28 x+10=0

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  10. If z1=2-i ,z2=1+i ,find |(z1+z2+1)/(z1-z2+i)|

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  11. If a + i b =((x+i)^2)/(2x^2+1),prove that a^2+b^2=((x^2+1)^2)/((2x^2+...

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  12. Let z1=2-i ,z2=-2+i. Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1/(z1 bar...

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  13. Find the modulus and argument of the complex number (1+2i)/(1-3i).

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  14. Find the real numbers x\ a n d\ y , if (x-i y)(3+5i) is the conjugate ...

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  15. Find the modulus of (1+i)/(1-i)-(1-i)/(1+i).

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  16. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

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  17. If alpha and beta are different complex number with |beta|=1, then f...

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  18. Find the number of non-zero integral solutions of the equation |1-i|^...

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  19. If (a + i b) (c + i d) (e + i f) (g + i h) = A + i B, then show that (...

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  20. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

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