# What is the Difference between imaginary part and imaginary number?

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• SHASHWAT PRATAP SING

#### SHASHWAT PRATAP SING

I am a high school student and I have a doubt regarding Complex Numbers.
when we define a complex number we say that a number of the form z=a+ib ,where a and b are real numbers is called a complex number.
a is called the real part and b is called the imaginary part, but I have a doubt here we know that ib is an imaginary number then why we say only b is the imaginary part of z why not ib.
for example-
In z=5+3i why we say 3 is the imaginary part of z why not 3i.

This is simply the way things are defined: the imaginary part of a complex number is a real number (the real number multiplying i .)
In fact the imaginary part of a pure imaginary number is a real number. These are just done to make the manipulations easier.

I am a high school student and I have a doubt regarding Complex Numbers.
when we define a complex number we say that a number of the form z=a+ib ,where a and b are real numbers is called a complex number.
a is called the real part and b is called the imaginary part, but I have a doubt here we know that ib is an imaginary number then why we say only b is the imaginary part of z why not ib.
for example-
In z=5+3i why we say 3 is the imaginary part of z why not 3i.
It's purely convention. The way things are defined we have: ##z = Re(z) +iIm(z)##, where ##Re(z), Im(z)## are real numbers. You could define ##Re(z) = a## and ##Im(z) = ib##. That wouldn't change anything except a detail about how you name things. For example, normally we have: $$|z|^2 = Re(z)^2 + Im(z)^2$$
Whereas, with your definition we would have: $$|z|^2 = Re(z)^2 + (\frac{Im(z)}{i})^2$$
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