UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations (सम्मिश्र संख्याएँ और द्विघातीय समीकरण)

These Solutions are part of UP Board Solutions for Class 11 Maths. Here we have given UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations (सम्मिश्र संख्याएँ और द्विघातीय समीकरण).

प्रश्नावली 5.1

प्रश्न 1 से 10 तक की सम्मिश्र संख्याओं में प्रत्येक को a + ib के रूप में व्यक्त कीजिए।

प्रश्न 1.
(5i) ([latex]\frac { -3 }{ 5 }[/latex] i)
हल:
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 1

प्रश्न 2.
i9 + i19
हल:
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 2

UP Board Solutions

प्रश्न 3.
i-39
हल:
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 3

UP Board Solutions

प्रश्न 4.
3(7 + i7) + i (7 + i7)
हल:
3(7 + i7) + i (7 + i7)
= 21 + 21i + 7i + 7i²
= 21 + 28i + 7(-1) [∵ i² = -1]
= 21 – 7 + 28i
= 14 + 28j

प्रश्न 5.
(1 – i) – (-1 + i6)
हल:
(1 – i) – (-1 + i6)
= (1 – i) + (1 – 6i) (UPBoardSolutions.com)
= 1 – i + 1 – 6i
= 2 – 7i

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 6

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 7

UP Board Solutions

प्रश्न 8.
(1 – i)4
हल:
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 8

प्रश्न 9.
([latex]\frac { 1 }{ 3 }[/latex] + 3i)3
हल:
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 9
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 9.1

प्रश्न 10.
(-2 – [latex]\frac { 1 }{ 3 }[/latex] i)3
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 10

UP Board Solutions

प्रश्न 11 से 13 तक की सम्मिश्र संख्याओं में प्रत्येक का गुणात्मक प्रतिलोम ज्ञात कीजिए।
प्रश्न 11.
4 – 3i.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 11

प्रश्न 12.
√5 + 3i.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 12

प्रश्न 13.
-i.
हल:
-1 का गुणात्मक प्रतिलोम
(UPBoardSolutions.com)
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 13

प्रश्न 14.
निम्नलिखित व्यंजक को a + ib के रूप में व्यक्त कीजिए:
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1 14

UP Board Solutions

प्रश्नावली 5.2

प्रश्न 1 से 2 तक सम्मिश्र संख्याओं में प्रत्येक का मापांक और कोणांक ज्ञात कीजिए:
प्रश्न 1.
z = -1 – i√3
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 1
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 1.1

प्रश्न 2.
-√3 + i.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 2

UP Board Solutions

प्रश्न 3 से 8 तक सम्मिश्र संख्याओं में प्रत्येक को ध्रुवीय रूप में रूपांतरित कीजिए:
प्रश्न 3.
1 – i
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 3
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 3.1

प्रश्न 4.
-1 + i.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 4

UP Board Solutions

प्रश्न 5.
-1 – i.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 5
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 5.1

प्रश्न 6.
-3.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 6

UP Board Solutions

प्रश्न 7.
√3 + i
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 7
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 7.1

प्रश्न 8.
i.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.2 8

UP Board Solutions

प्रश्नावली 5.3

निम्नलिखित समीकरणों में से प्रत्येक को हल कीजिए:
प्रश्न 1.
x² + 3 = 0.
हल:
x² + 3 = 0 या x² = -3 या x = ± √-3 = ± √3 i.

प्रश्न 2.
2x² + x + 1 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 2
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 2.1

प्रश्न 3.
x² + 3x + 9 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 3

UP Board Solutions

प्रश्न 4.
-x² + x – 2 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 4

प्रश्न 5.
x² + 3x + 5 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 5
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 5.1

UP Board Solutions

प्रश्न 6.
x² – x + 2 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 6

प्रश्न 7.
√2 x² + x + √2 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 7

UP Board Solutions

प्रश्न 8.
√3 x² – √2 x + 3√3 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 8

प्रश्न 9.
x² + x + [latex]\frac { 1 }{ \surd 2 }[/latex] = 0
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 9

UP Board Solutions

प्रश्न 10.
x² + [latex]\frac { x }{ \surd 2 }[/latex] + 1 = 0
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.3 10

अध्याय 5 पर विविध प्रश्नावली

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 1
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 1.1

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 2

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 3

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 4
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 4.1

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5

UP Board Solutions
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 5.1

प्रश्न 6 से 9 में दिए गए प्रत्येक समीकरण को हल कीजिए:

प्रश्न 6.
3x² – 4x + [latex]\frac { 20 }{ 3 }[/latex] = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 6

UP Board Solutions
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 6.1

प्रत 7.
x² – 2x + [latex]\frac { 3 }{ 2 }[/latex] = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 7

प्रश्न 8.
21x² – 28x + 10 = 0.
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 8UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 9

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 10

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 11

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 11.1

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 12
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 12.1

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 12.2

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 13
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 13.1
UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 13.2

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 14

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 15

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 16

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 17

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 18

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 19

UP Board Solutions

UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations 20

We hope the UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations (सम्मिश्र संख्याएँ और द्विघातीय समीकरण) help you. If you have any query regarding UP Board Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations (सम्मिश्र संख्याएँ और द्विघातीय समीकरण), drop a comment below and we will get back to you at the earliest.

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