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Represent the complex numbers (1+7i)...

Represent the complex numbers
`(1+7i)/((2-i)^(2))` in polar form

A

`sqrt2(cos"(3pi)/4-isin"" (3pi)/4)`

B

`sqrt2(cos"(3pi)/4+isin"" (3pi)/4)`

C

`sqrt2(cos"(7pi)/4+isin"" (7pi)/4)`

D

`sqrt2(cos"(7pi)/4-isin"" (7pi)/4)`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. The sum of principal arguments of complex numbers 1+i,-1+isqrt3,-sqrt3...

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  2. If z=cospi/4+isinpi/6 , then |z|=1, arg(z)=\ pi/4 b. |z|=1, arg(z)=\ p...

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  3. Represent the complex numbers (1+7i)/((2-i)^(2)) in polar form

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  4. In any DeltaABC,if cos theta =(a)/(b+c) , cos phi =(b)/(a+c) , cos P...

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  5. The value of (i+sqrt3)^(100)+(i-sqrt3)^(100)+2^(100) is

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  6. Which of the following is not true ?

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  7. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

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  8. Let a=i^i and consider the following statements S1: a=e^(-pi/2), S2:T...

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  9. If z^(2)+z+1=0 then the value of (z+1/z)^(2)+(z^(2)+1/z^(2))^(2)+(z...

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  10. If omega is an imaginary fifth root of unity, then find the value of l...

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  11. If 1,alpha1,alpha2,alpha3,.........,alpha(3n) be the roots of the equt...

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  12. If z(1),z(2),z(3),z(4) are two pairs of conjugate complex numbers, th...

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  13. If |z-4 +3i| le 2 then the least and the greatest values of |z| are q

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  14. If |z1|=2,|z2|=3,|z3|=4 and |2z1+3z2+4z3|=4 then the expression |8z2z3...

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  15. If z1 = cos theta + i sin theta and 1,z1,(z1)^2,(z1)^3,.....,(z1)^(n-1...

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  16. The area of the triangle whose vertices are represented by the complex...

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  17. The maximum value of |z| where z satisfies the condition |z+(2/z)|=2 i...

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  18. The value of (1-tan^(2)15^(@))/(1+tan^(2)15^(@)) is

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  19. Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are ...

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  20. If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2, then the locus of z is

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