Published On: Sat, Aug 10th, 2019

## Some Basic Problems

Basic operations with complex numbers through simple problem

Problem 1.

If:

A = a + j b;

A = 0 + j1;  A = 1 + j 0;  A = -1 + j 0;  A = 0 – j 1;

A = 0 + j ²;   A = 1 + j ²;   A = -1 + j ²;   A = 0 – (- j ²);

A = 0 +1/ j ²;   A = 1 + 1/ j ²;   A = -1 + 1/ j ²;   A = 0 – (1/ j ²);

A = 0 + 1/- j ²;  A = 1 +1/- j ²;  A = -1 + 1/- j ²;  A = 0 – 1/- j ²;

A =  j;  A =  j ²;  A =- j ;  A =- j ² ; A = 1/ j ;   A = 1/ j ²;  A

= -( 1/ j ²);   A = 1/- j ² ; A = -(1/- j ²) ;

And,

B = c + j d;

B = 0 + j1;  B = 1 + j 0;  B = -1 + j 0;  B = 0 – j 1;

B = 0 + j ²;   B = 1 + j ²;   B = -1 + j ²;   B = 0 – (- j ²);

B = 0 +1/ j ²;   B = 1 + 1/ j ²;   B = -1 + 1/ j ²;   B = 0 – (1/ j ²);

B = 0 + 1/- j ²;  B = 1 +1/- j ²;  B = -1 + 1/- j ²;  B = 0 – 1/- j ²;

B =  j;  B =  j ²;  B =- j ;  B =- j ² ;  B = 1/ j ;  B = 1/ j ²;

B = -( 1/ j ²);   B = 1/- j ² ; B = -(1/- j ²) ;

Find the values:

1. In rectangular forms,
2. In exponential forms,
3. In polar forms,
4. Show all results in Gauss and Polar plane.

Note, Solve step-by-step strictly!

A + B

B + A

A – B

B – A

A x B

A/B

B/A

A* + B

A + B*

A* – B

A – B*

1/A

1/B