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Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(1...

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

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The correct Answer is:
1 +4i
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simplify the following 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)

Write the following in the form x+iy: (i) (3+2i)(2-i) (ii) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25) . (iii) ((3-2i)(2+3i))/((1+2i)(2-i)) .

Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .

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

6i^(50) + 5i^(33) - 2i^(15) + 6i^(48) = 7i .

Find the value of i+i^(2)+i^(3)+i^(4)

Find the value of 1+i^(2)+i^(4)+i^(6)+i^(8)+...+i^(24)

Find the value of 1+i^(2)+i^(4)+i^(6)+i^(8)+...+i^(24)

Find the value of ( i^2 + i^4 + i^6 + i^7 ) / ( 1 + i^2 + i^3 ) is ( a ) 1 - i ( b ) 1 + i ( c ) 2 - i ( d ) 2 + i

AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Try Yourself
  1. Evaluate 2i^(2)+ 6i^(3)+3i^(16) -6i^(19) + 4i^(25)

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  2. Evaluate [ i^(14) - (1/i)^(34)]^2

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  3. Plot the complex number -4 + 5i on the Argand plane.

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  4. Plot the complex number -3 + 7i on the Argand plane.

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  5. Write the complex number represented by the point (-2,5)

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  6. Write the complex number represented by the point (-6,-7)

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  7. Find the values of x and y , if (3y -2) + (5 -4x)i=0 , where , x y i...

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  8. Find the values of x and y , if x + 4yi = ix + y + 3 where x ,y in ...

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  9. If z(1) = 4 -I and z(2) = - 3 + 7i then find (i) z(1) +z(2) (...

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  10. If z(1) = 6 + 9i and z(2) = 5 + 2i then find z(1)/z(2)

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  11. if z= 1 +i, z(2)= 2 -3i and z(3) = 5+ 2i then find z(1)-z(2)+3z(3)

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  12. if z(1)=2+3i, z(2)=1-iand z(3) = 3+ 4i,then find z(1)z(2) +z(3)

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  13. if z(1) =-1 + 3i and z(2)= 2 + i then find 2(z(1) +z(2))

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  14. find the multiplicative inverse of the complex number 2 + 9i .

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  15. Express ( 4 - 5/2 i)^(2) in the form of a + ib.

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  16. express (1 -i)^(4) in the form of a +ib.

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  17. Express ( 1/3 + 4/3 i)^(2) in the form of a + ib.

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  18. if z(1) = 3i and z(2) =1 + 2i , then find z(1)z(2) -z(1)

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  19. Express 1/(1+cos theta-i sin theta) in the form of a +ib.

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  20. Express (1 /(2 -2i)+3/(1+i)) ((3+ 4i)/(2-4i)) in the form of a +ib

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