HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

If |z| = 2 show that the 8 ≤ |z + 6 + 8i| ≤ 12

If z₁, z₂ and z₃ are three complex numbers such that |z₁| = 1, |z₂| = 2, |z₃| = 3 and |z₁ + z₂ + z₃| = 1, show that |9z₁z₂ + 4z₁z₃ + z₂z₃| = 6

If the area of the triangle formed by the vertices z, iz, and z + iz is 50 square units, find the value of |z|

Show that the equation `z^3 + 2bar(z)` = 0 has five solutions

Find the square roots of 4 + 3i

Find the square roots of – 6 + 8i

Find the square roots of – 5 – 12i

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If = `((sqrt(3) + "i")^3 (3"i" + 4)^2)/(8 + 6"i")^2`, then |z| is equal to

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If z is a non zero complex number, such that 2iz² = `bar(z)` then |z| is

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If |z – 2 + i| ≤ 2, then the greatest value of |z| is

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If (1 + i)(1 + 2i)(1 + 3i) ……. (l + ni) = x + iy, then 2.5.10 …… (1 + n²) is

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If α and β are the roots of x² + x + 1 = 0, then α²⁰²⁰ + β²⁰²⁰ is

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The value of `((1 + sqrt(3)"i")/(1 - sqrt(3)"i"))^10` is

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If f and g are polynomials of degrees m and n respectively, and if h(x) = (f o g)(x), then the degree of h is

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A polynomial equation in x of degree n always has

Find the domain of the following functions:

`tan^-1 (sqrt(9 - x^2))`

Find the domain of the following functions:

`1/2 tan^-1 (1 - x^2) - pi/4`

Find the value of `tan^-1(tan  (5pi)/4)`

Find the value of `tan^-1 (tan(- pi/6))`

Find the value of `tan(tan^-1((7pi)/4))`