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Mathematics | Complex Numbers

Algebraic Operations on Complex Numbers Imaginary Number i and its properties Polar form of Complex Numbers Properties of Complex Numbers Roots of Unity
If x and y are real number then choose the correct option:
If z = x + i y is a complex number, then the value of expression [sinh x.cosh (iy) + cosh x.sinh (iy)] will be: 
Let p be the conjugate of the complex number q = x + iy . Find the value of pq. 
If m, n, p, q are consecutive integers then the value of im ⋅ in ⋅ ip ⋅ iq is
If m, n, p, q are consecutive integers then the value of iminipiq is
If 4x + i(3x -y) = 3 + i(- 6) where x and y are real numbers then find the values of x and y ?
Find the magnitude of (z̅ + z), z = 8i - 5 Where z is a complex number and z̅ is the conjugate of z
Find value of i10 ? Where \(\rm i = \sqrt{-1}\) .
Find the value of x and y for which (3 + 4i) x2 – (4 – 3i) y = 3x – 4y + 6i, where x, y ∈ R.
What is the value of (i2 + i4 + i6 +... + i2n), Where n is even number.
What is i1000 + i1001 + i1002 + i1003 equal to (where i \(= \sqrt { - 1}\))?
If x = 1 + i, then what is the value of x6 + x4 + x2 + 1?
What is the value of ii?
Which axis is known as real and imaginary axis in argand plane?
Consider the following statements in respect of an arbitrary complex number Z: 1. The difference of Z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate is a real number. Which of the above statements is/are correct?
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