Convert the complex number in the polar form: -3 - Vidyadip

Question

Convert the complex number in the polar form: $-3$

✓

Answer

Here $z = -3 = r(\cos \theta + i\sin \theta )$
$ \Rightarrow r\;\cos \theta = - 3$ and $r\;\sin \theta = 0$
Squaring both sides of (i) and adding
${r^2}({\cos ^2}\theta + {\sin ^2}\theta ) = 9 + 0$$ \Rightarrow {r^2} = 9 \Rightarrow r = 3$
$\therefore 3\cos \theta = - 3$ and $3\sin \theta = 0$
$ \Rightarrow \cos \theta = - 1$ and $\sin \theta = 0$
Since $\sin \theta $ is positive and $\cos \theta $ is negative
$\therefore \theta $ lies in second quadrant
$\therefore\theta=(\pi-0)\;=\;\mathrm\pi$
Hence polar form of z is $3(\cos \pi + i\sin \pi )$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from COMPLEX NUMBERS AND QUADRATIC EQUATIONS→COMPLEX NUMBERS AND QUADRATIC EQUATIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0) Focus (3, 0)

Show that the area of the triangle formed by the lines $y = m_1 x + c_1 , y = m_2x + c_2$ and $x = 0$ is $\frac{\left(c_{1}-c_{2}\right)^{2}}{2\left|m_{1}-m_{2}\right|}$

A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is: A black king.

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum: $x^2 = 6y$

Find the equation of the circle having $(1, −2)$ as its centre and passing through the intersection of the lines $3x + y = 14$ and $2x + 5y = 18.$

Prove that: $\cos\Big(\frac{\pi}{4}+\text{x}\Big)-\cos\Big(\frac{\pi}{4}-\text{x}\Big)=\sqrt2\cos\text{x}$

Find the slope of a line:

Which bisects the first quadrant angle.
Which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

There are 10 persons named $P _1, P _2, P _3, \ldots, P _{10}$. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement $P_1$ must occur whereas $P_4$ and $P_5$ do not occur. Find the number of such possible arrangements.

Describe the following sets in set-builder form: D = {10, 11, 12, 13, 14, 15};

There are four men and, six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?