If we subtract, from a complex number, its conjugate then the result will be purely a
The product of a complex number z and its conjugate z̄ is:
If a complex number z = x + iy, then x can be written in terms of z and its conjugate z̄ as:
De Moivre's theorem states that: (cos θ + i sin θ)ⁿ =
If a complex number z = a + ib, then the argument (or amplitude) of z is given by:
z + z̄ = 0 if and only if:
If 3x + (y − 2)i = (5 − 2x) − (3y − 8)i, then (x, y) is
If the square of a number x is i, then x =
(2 − 3i)² − 2(2 − 3i) + 9 =
If x + iy = (3 + 2i)(3 − 2i), then x and y are equal to:
**13.** If (2 + 5i)/(1 − i) = x − yi, then x and y are:
3|cos(π/6) + i sin(π/6)|⁻¹ =
If z = cos(1/√2) + i sin(√2), then the real part of z is:
Adding (x + yi) to (6 + 2i) gives the zero complex number. The values of x and y are:
The multiplicative inverse of (√3, √2) is:
The modulus of (3 + i)(4 + i) is:
The modulus of 2(cos(π/3) + i sin(π/3)) is:
