Practice Question (Unsolved) For NDA | Practice question (Unsolved) For IIT JEE | Complex Number Practice Question Unsolved

Practice Question (Unsolved) For NDA | Practice question (Unsolved) For IIT JEE | Complex Number Practice Question Unsolved | assignment question

Practice question For Complex Number

1.If w is a complex cube root of unity and x² = w² - w -2 , then what is the value of x² + 4x + 7 ?
2. If z is complex number such that z + z^-1 = 1 , then what is the of z⁹⁹ + z^-99 ?
3. If the point z₁ = 1 + i is the reflection of the point z₂ in the line iz - iz = 5 , what is the point z₂ ?
4. What is the real part of (sinx + icosx)³ ?
5. If x = a + b , y = aα + bβ , z = aβ + bα , where α and β are complex cube root of unity , then show that xyz = a³ + b³.
6. Let z be the complex number such that |z| + z = 3 + i , what is the value of |z| ?
7. Find the condition for which the complex number sinx + icos2x and cosx - isin2x are conjugate to each other ?
8. For all complex number z₁ , z₂ , satisfying |z₁| = 12 and |z₂ - 3- 4i | = 5 , what is the minimum value of |z₁ - z₂ | ?
9. If iz³ + z² -z + i = 0 , then show that |z| = 1.
10. If z₁ and z₂ are two non zero complex numer such that |z₁ + z₂ | = | z₁ | + | z₂ | , then what is the value of arg(z₁ ) - arg(z₂) ?

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NDA Exam | NDA syllabus | Agniveer | UPSC | NDA Paper Pattern | NDA notification

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Learn New English words to improve your vocabulary Words for 7rd November 2023 Word Meaning Insouciant free from worry , anxiety Featly neatly Heartsease peace of mind Aliferous having wings Whelve to hide Words for 3rd November 2023 Word Meaning Affable Someone who is friendly , easily approachable and welcoming Palatable Pleasant and good Panache confidence or behavoiur that is very impressive Pizzazz Attractive and lively Splurge to spend money extravagantly Words for 1st November 2023 Word Meaning Oblivescene The process of forgetting Stolid Unemotional Busticate to break into pieces Luddite Someone who is opposed or ...

Start the test Question no. 1 Let z, w be complex numbers such that z + i w =0 and arg zw =π . Then arg z equals π/4 5π/4 3π/4 π/2 Question no. 2 If z and w are two non-zero complex number such that |zw|=1, and Arg (z)-Arg(w)=π/2 , then z¯w is equal to 1 -1 -i i Question no. 3 If |z+4|<= 3, then the maximum value of |z+1| is 4 10 6 0 Question no. 4 The conjugate of complex number is 1/(i-1), then that complex number is 1/(i+1) -1/(i+1) 1/(i-1) -1/(i-1) Question no. 5 What are the square roots of -2i ? ∓(1+i) ∓(1-i) ∓i ∓1 Question no. 6 What is the value of the sum of i 2i -2i 1+i Question no. 7 What is the number of distinct solution of the equation z 2 + |z| = 0 (where z i...

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Practice question On Eigen values and Eigen vectors Linear Algebra | Matrix algebra | GATE | UPSC | IES | Engineering

Linear Algebra Question no. 1 What are the eigen values of ? looks_one 1,4 looks_two 2,3 looks_3 0,5 looks_4 1,5 Answer Option looks_3 0,5 Solution Solution : ( 4 - λ)(1 - λ) - 4 = 0 λ 2 - 5λ + 4 - 4 = 0 λ 2 - 5λ = 0 λ(λ - 5) = 0 λ = 0 , 5 Question no. 2 What is the eigenvalues of the matrix ? looks_one 1, 4 ,4 looks_two 1 , 4 ,-4 looks_3 3 , 3 ,3 looks_4 1 , 2 ,6 Answer option looks_one 1, 4 ,4 Solution Solution : ( 3 - λ )[(3-λ) 2 -1] + 1(-3 + λ -1 ) - 1(1+3 -λ) = 0 ( 3 - λ )(9 + λ 2 - 6λ -1 ) + 2( λ - 4 ) = 0 ( 3 - λ )( λ 2 - 6λ + 8 ) + 2( λ - 4 ) = 0 ( 3 - λ )( λ - 4)( λ - 2) + 2( λ - 4 ) = 0 (λ - 4) [( 3 - λ )( λ - 2) + 2 ] = 0 (λ - 4) (λ 2 - 5λ + 4) = 0 (...

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Complex Number | free study material for IIT-JEE , NDA and Airforce

Complex Number ⚫What is Complex number ? ⚪ Combination form of real and imaginary number z = a + ib where i(iota) = √ -1 ⚫ Integer power of i (√ -1 ) (a) i 4n = 1 (b) i 4n+1 = i (c) i 4n+2 = -1 (d) i 4n+3 = -i ⚫ Equality of two complex numbers ⚪ Two complex number z 1 = x 1 + iy 1 and z 2 = x 2 + iy 2 are said to be equal if and only if their real and imaginary parts are separately equal. z 1 = z 2 ⇔ x 1 + iy 1 = x 2 + iy 2 ⇔ x 1 = x 2 and y 1 = y 2 ⚫ Conjugate of a complex number : ⚪ For any complex number z = a + ib , then its conjugate is defined as z = a - ib ⚪ Geometrically , the conjugate of z is the reflection or point image of z in the real axis. ⚫ Properties of conjugate : ⚪ z̿ = z ⚪ ⚪ ⚪ ⚪ ⚪ ⚪ ⚪ z + z̅ = 2Re(z) = purely real ⚪ z - z̅ = ...

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