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

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

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

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  2. For any two complex numbers z1and z2, prove that R e(z1z2)=R ez1R e z2...

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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 under root of (a+i b)/(c+i d)=x+i y , Prove (a^2+b^2)/(c^2+d^2)=(x...

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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. Solve the equation :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. If z1=2-i ,\ +2=-2+i , find : R e((z1z2)/(z1))

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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 and y if (x-i y)(3+5i)is the conjugate of -6-...

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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 alphaand betaare different complex numbers with |beta|=1,then fin...

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  18. Find the number of non-zero integral solution of the equation |1-i|^x=...

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  19. If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a^2 +...

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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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