## 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.