How do you find a complex number in polar form

Hello welcome to chafia physic. In this post i just want to share with you some problem that related with complex number and How to find a complex Number in polar Form. In this post we will also discussing about Function of complex variable with some sample question related with it. Ok first let's we start discussing about a complex number.

A.Origin of Complex Number

During our time in school we faced so many function and equation that describe something. Just for an example: we can describe free fall motion with quadratic equation like this.

 if x is t and a is -g now we can find how long a ball or a thing, fallen from initial heigth c. Now lets just focusing on quadratic equation. In this equation we can find x with abc formula, and from the abc formula we will get to value of x related with equation.
Suppose we set the equation and get b quared is less than 4ac.

As yo can see, in our x now containt i, where i is square root of -1. i is imaginary number, this number is different with real number we know so far. You cant draw or plot i in real cartesian coordinate. So you need a new coordinate and a new definition to describe this situation. And the thing that we need is ... Yap Complex number.
In complex number both real and imaginary part are include in one set of equation. Suppose Complex number is z, so we can write the equation to be
Z = x + iy
where x is the real part, and y is imaginary part. Always rememmber y in complex number is different with y in real. So when we analyze z = x+iy, honestly we just analyze x with imaginary part.

B. Problem and Answer Complex Number

To be more familliar with complex number, now we will solve some problem related with it.

Suppose we have z1 = 2+i and z2 =5i  , and then all of the complex number operation will be.

Addition Operation:

Substraction Operation:

Multipication Operation:

Division Operation:
Special for division, we cant just devide z1/z2 directly. Its because in both z1 and z2 has i in the equation. So we must using Special Trick to solve it.
Now i want to introduce you with conjugate of complex numeber (z*). Suppose you have z = x+iy, conjugate of z is z* = x-iy. In here conjugate is number that has opposite sign or direction in imaginary part. Ok let using it in division operation.

 Ok thats all for complex number in complex plane, lets move to another cases in complex number.

C.Complex Number in Polar Form

In real number we can transform x and y cartesian coordinate to be r and teta polar coordinate. For complex number we can also do the same thing. To transform complex number look at the picture below.

In here we have x and y complex transform to r and teta equation. Now we must subtitute x and y to z, to get final form of polar complex number.

In here r is equal to the magnitude of z, so we cand find r with.

Now we have all of the thing to transform complex number to polar. Next we will solve some problem related with it.

Example 1:
Suppose we have z = 2+i , now transform it to polar form.

After we get r now find teta.

From calculation we have complete form of polar z = 2+i to be.

Example 2:
Suppose we have z = 1/(1+i) , find the polar form of z.

Now find r from z.

Next find teta of z.

And Finally we get z equation in polar form to be.

Example 3:
Suppose we have z =  , find z in polar form.

Here we will solve za polar form first and then we subtitute za form to z.

Oke i think thats all for this post. I hope it can help you to answer your question of How do you find a complex Number in polar form.
 Dont forget to share this post to your friend, and lets just ask any quaestion related with complex number in comment section below.

See you in next post, Thank you ...