Popular Complex Numbers Questions

For positive integers n1 and n2 , the value of the expression (1+i)n1+(i+13)n1+(i+15)n2+(i+17)n2 here i= -1 is real if and only if (A)n1=n2+1 (B) n1=n2-1 (C) n1=n2 (D)n1>0,n2 >0 pl post the soln as well . ...

For x ε (0, π/2) and sin x = 1/3, if \sum_{n=0}^{\infty }\frac{sin(nx)}{3^{n}}=\frac{a+b\sqrt{b}}{c} then find the value of (a + b + c), where a, b, c are positive integers. ...

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The value of i log(x – i) + i2+i3 log(x +i) + i4( 2 tan-1x), x> 0 is (A) 0 (B) 1 (C) 2 (D) 3 ...

If 'a' is a complex number such that |a|=1.Find the values of a,so that equation az2+z+1=0 has one purely imaginary root. ...

\hspace{-16} $ Minimum value of $\bf{\left|z-1-i \right| + \left |z+2-3i \right| + \left |z+3+2i \right|}$\\\\\\ where $\bf{z = x+iy}$ and $\bf{i = \sqrt{-1}}$ ...

Argument and modulus of frac{{1 + i}}{{1 - i}} are respectively ...

If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, prove that arg(z1/z4) + arg(z2/z3) = 0. ...

If frac{{c + i}}{{c - i}} = a + ib, where a, b, c are real, then {a^2} + {b^2} = ...

sqrt 3Â + i = ...

If {( - 7 - 24i)^{1/2}} = x - iy, then {x^2} + {y^2} = ...

A square root of 2i is ...

For a positive integer n, the expression {(1 - i)^n}{left( {1 - frac{1}{i}} ight)^n} equals ...

The value of {i^{1 + 3 + 5 + ... + (2n + 1)}} is ...

The least positive integer n which will reduce {left( {frac{{i - 1}}{{i + 1}}} ight)^n} to a real number, is ...

If x + frac{1}{x} = sqrt 3 , then x = ...

{i^2} + {i^4} + {i^6} + ..... upto (2n+1) terms = ...

If {left( {frac{{1 + i}}{{1 - i}}} ight)^m} = 1, then the least integral value of m is ...

The values of x and y satisfying the equation frac{{(1 + i),x - 2i}}{{3 + i}} + frac{{(2 - 3i),y + i}}{{3 - i}} = i, are ...