Thread: Complex Numbers

Put the following expressions into the shape with .

(a)

(b)

The answers should be:

(a)

(b)

I know that the real and imaginary parts of a+ib are a and b respectively. But I don't know how to arrive at this answers, can anyone please explain? Thanks.

Originally Posted by demode

Put the following expressions into the shape with .

(a)

(b)

The answers should be:

(a)

(b)

I know that the real and imaginary parts of a+ib are a and b respectively. But I don't know how to arrive at this answers, can anyone please explain? Thanks.

Remember the defintion of i is

For the first

For the 2nd just distribute and use the property above.

Originally Posted by TheEmptySet

Remember the defintion of i is

For the first

For the 2nd just distribute and use the property above.

Thank you, that helps a lot. But I don't understand why ! When I look at the imaginary-real axis, on the imaginary axis corresponds to 1 on the real axis. That's why I thought .

Originally Posted by demode

Thank you, that helps a lot. But I don't understand why ! When I look at the imaginary-real axis, on the imaginary axis corresponds to 1 on the real axis. That's why I thought .

by DEFINITION of imaginary and complex numbers.


This is because they needed to create a number (i.e. out of their imaginations) that . They called this number .


So if then that must mean .