Complex Numbers Class 11 Lecture 3


The Man Who Has Confidence In Himself Gains The Confidence Of Others. – Hasidic Proverb

Lecture - 3 Chapter 5 Complex Numbers

Conjugate of a complex number,  Relationship of conjugate with modulus of complex numbers

Example 8. Convert the complex number \(\frac{-16}{1+i \sqrt{3}}\) into polar form.

Example 12.  Find the conjugate of \( \frac{(3-2i)(2+3i)}{(1+2i)(2-i)}\)

Example 14. If \(x+iy=\frac{a+ib}{a-ib}\), prove that \(x^2+y^2=1\).

Example 15. Find real \( \theta \) such that \(\frac{3+2i \sin \theta}{1-2i \sin \theta}\) is purely real and purely imaginary.

Example 16. Convert the complex number \(z = \frac{i-1}{\cos \frac{\pi}{3} + i  \sin \frac{\pi}{3} }\) in the polar form.