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NCERT solutions Mathematics Class 11 chapter 5 Complex Numbers and Quadratic Equations

Chapters

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

Chapter 5 - Complex Numbers and Quadratic Equations

Pages 103 - 104

Express the given complex number in the form a + ib: `(5i) (- 3/5 i)`

Q 1 | Page 103

Express the given complex number in the form a + ibi9 + i19

Q 2 | Page 103

Express the given complex number in the form a + ibi–39

Q 3 | Page 103

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

Q 4 | Page 104

Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)

Q 5 | Page 104

Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`

Q 6 | Page 104

Express the given complex number in the form a + ib : `[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`

Q 7 | Page 104

Express the given complex number in the form a + ib:  (1 – i)4

Q 8 | Page 104

Express the given complex number in the form a + ib: `(1/3 + 3i)^3`

Q 9 | Page 104

Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`

Q 10 | Page 104

Find the multiplicative inverse of the complex number 4 – 3i

Q 11 | Page 104

Find the multiplicative inverse of the complex number `sqrt5 + 3i`

Q 12 | Page 104

Find the multiplicative inverse of the complex number –i

Q 13 | Page 104

Express the following expression in the form of a + ib.

`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`

Q 14 | Page 104

Page 108

Find the modulus and the argument of the complex number  `z = – 1 – isqrt3`

Q 1 | Page 108

Find the modulus and the argument of the complex number `z =- sqrt3 + i`

Q 2 | Page 108

Convert the given complex number in polar form: 1 – i

Q 3 | Page 108

Convert the given complex number in polar form: – 1 + i

Q 4 | Page 108

Convert the given complex number in polar form: – 1 – i

Q 5 | Page 108

Convert the given complex number in polar form: –3

Q 6 | Page 108

Convert the given complex number in polar form `sqrt3 + i`

Q 7 | Page 108

Convert the given complex number in polar form: i

Q 8 | Page 108

Page 109

Solve the equation x2 + 3 = 0

Q 1 | Page 109

Solve the equation 2x2 + x + 1 = 0

Q 2 | Page 109

Solve the equation x2 + 3x + 9 = 0

Q 3 | Page 109

Solve the equation –x2 + x – 2 = 0

Q 4 | Page 109

Solve the equation x2 + 3x + 5 = 0

Q 5 | Page 109

Solve the equation `x^2 + x + 1/sqrt2 = 0`

Q 5.3 | Page 109

Solve the equation x2 – x + 2 = 0

Q 6 | Page 109

Solve the equation  `sqrt2x^2 + x + sqrt2 = 0`

Q 7 | Page 109

Solve the equation  `sqrt3 x^2 - sqrt2x + 3sqrt3 = 0`

Q 8 | Page 109

Solve the equation  `x^2 + x/sqrt2 + 1 = 0`

Q 10 | Page 109

Pages 112 - 113

Evaluate : `[i^18 + (1/i)^25]^3`

Q 1 | Page 112

For any two complex numbers z1 and z2, prove that Re (z1z2) = Re zRe z2 – Im z1 Im z2

Q 2 | Page 112

Reduce  `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.

Q 3 | Page 112

If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`

Q 4 | Page 112

Convert the following in the polar form:

`(1+7i)/(2-i)^2`

Q 5.1 | Page 112

Convert the following in the polar form:

`(1+3i)/(1-2i)`

Q 5.2 | Page 112

Solve the equation `3x^2 - 4x + 20/3 = 0`

Q 6 | Page 112

Solve the equation   `x^2 -2x + 3/2 = 0`  

Q 7 | Page 112

Solve the equation   `x^2 -2x + 3/2 = 0`  

Q 7 | Page 112

Solve the equation 27x2 – 10+ 1 = 0

Q 8 | Page 112

Solve the equation 21x2 – 28+ 10 = 0

Q 9 | Page 113

If z1 = 2 – i,  z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`

Q 10 | Page 113

If a + ib  = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`

Q 11 | Page 113

Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`

Q 12.1 | Page 113

Let z1 = 2 – i, z2 = –2 + i. Find `Im(1/(z_1barz_1))`

Q 12.2 | Page 113

Find the modulus and argument of the complex number `(1 + 2i)/(1-3i)`

 
Q 13 | Page 113

Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

Q 14 | Page 113

Find the modulus  of  `(1+i)/(1-i) - (1-i)/(1+i)`

Q 15 | Page 113

If (x + iy)3 = u + iv, then show that `u/x + v/y  =4(x^2 - y^2)`

Q 16 | Page 113

If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`

Q 17 | Page 113

Find the number of non-zero integral solutions of the equation `|1-i|^x  = 2^x`.

 
Q 18 | Page 113

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.

Q 19 | Page 113

if `((1+i)/(1-i))^m` =   1, then find the least positive integral value of m.

Q 20 | Page 113

NCERT Mathematics Class 11

Mathematics Textbook for Class 11
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