Lecture-1

Complex Numbers Lecture 1
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Basics of numbers systems, imaginary numbers, real numbers, iota, Meaning of complex numbers, Working with Imaginary Numbers (iota), Working with Complex Numbers, Addition and Subtraction of Complex Numbers, Multiplication of Complex Numbers, Division of Complex Numbers, Additive Inverse and Multiplicative Inverse of Complex numbers

NCERT EXERCISE 5.1

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.

Question 1. (5i) \left ( -\frac{3}{5}i \right )

Question 2. i^9+i^{19}

Question 3. i^{-39}

Question 4. 3(7+i7)+i(7+i7)

Question 5. (1-i)-(-1+i6)

Question 6. \left ( \frac{1}{5} + i \frac{1}{5} \right ) – \left ( 4 + i \frac{5}{2} \right )

Question 7. \left [ \left ( \frac{1}{3} + i \frac{7}{3} \right ) + \left ( 4 + i \frac{1}{3} \right ) \right ] – \left ( – \frac{4}{3} + i \right )

Question 8. (1-i)^4

Question 9. \left ( \frac{1}{3} + 3i \right )^3

Question 10. \left ( -2 – \frac{1}{3} i \right )^3

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13.

Question 11. 4-3i

Question 12. \sqrt{5}+3i

Question 13. -i

Question 14. Express the following expression in the form of a+ib: \frac{(3+i\sqrt{5})(3-i\sqrt{5})}{(\sqrt{3}+\sqrt{2}i)-(\sqrt{3}-i \sqrt{2})}

NCERT EXERCISE 5.3

Solve each of the following equations:

Question 1. x^2+3=0

Question 2. 2x^2+x+1=0

Question 3. x^2+3x+9=0

Question 4. -x^2+x-2=0

Question 5. x^2+3x+5=0

Question 6. x^2-x+2=0

Question 7. \sqrt{2}x^2+x+\sqrt{2}=0

Question 8. \sqrt{3}x^2-\sqrt{2}x+3\sqrt{3}=0

Question 9. x^2+x+\frac{1}{\sqrt{2}}=0

Question 10. x^2+\frac{x}{\sqrt{2}}+1=0