NCERT Solutions
Class 11 - Mathematics - Chapter 4: COMPLEX NUMBERS AND QUADRATIC EQUATIONS
EXERCISE 4.1

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Question. 1

Express the complex number \((5i)\left(\dfrac{-3 - i}{5}\right)\) in the form \(a + ib\).

Answer:

\(3 + i0\)

Question. 2

Simplify and express in the form \(a + ib\): \(i^9 + i^{19}\).

Answer:

\(0 + i0\)

Question. 3

Express the value of \(i^{-39}\) in the form \(a + ib\).

Answer:

0 + i1

Question. 4

Express \(3(7 + i7) + i(7 + i7)\) in the form \(a + ib\).

Answer:

14 + 28i

Question. 5

Express \((1 - i) - (-1 + i6)\) in the form \(a + ib\).

Answer:

2 - 7i

Question. 6

Express \(\left(\dfrac{1}{5} + i\dfrac{2}{5}\right) - \left(4 + i\dfrac{5}{2}\right)\) in the form \(a + ib\).

Answer:

-\dfrac{19}{5} - \dfrac{21i}{10}

Question. 7

Express \(\left(\dfrac{1}{3} + i\dfrac{7}{3}\right) + \left(4 + i\dfrac{1}{3}\right) - \left(-\dfrac{4}{3} + i\right)\) in the form \(a + ib\).

Answer:

\dfrac{17}{3} + i\dfrac{5}{3}

Question. 8

Find \((1 - i)^4\) and express it in the form \(a + ib\).

Answer:

-4 + i0

Question. 9

Find \(\left(\dfrac{1}{3} + 3i\right)^3\) and express it in the form \(a + ib\).

Answer:

-\dfrac{242}{27} - 26i

Question. 10

Find \(\left(-2 - \dfrac{1}{3}i\right)^3\) and express it in the form \(a + ib\).

Answer:

-\dfrac{22}{3} - i\dfrac{107}{27}

Question. 11

Find the multiplicative inverse of the complex number \(4 - 3i\).

Answer:

\dfrac{4}{25} + i\dfrac{3}{25}

Question. 12

Find the multiplicative inverse of the complex number \(\sqrt{5} + 3i\).

Answer:

\dfrac{\sqrt{5}}{14} - i\dfrac{3}{14}

Question. 13

Find the multiplicative inverse of the complex number \(-i\).

Answer:

0 + i1

Question. 14

Express the expression \(\dfrac{(3 + i\sqrt{5})(3 - i\sqrt{5})}{(\sqrt{3} + \sqrt{2}i)(\sqrt{3} - i\sqrt{2})}\) in the form \(a + ib\).

Answer:

0 - i\dfrac{7\sqrt{2}}{2}