This shorthand is read as a vector magnitude A operating or pointing in the direction 0. It is termed the polar representation of a vector as shown in Figure III.2.

Now the function e j 0 may be expressed or resolved into its horizontal and vertical components in the complex plane:

The vector has been resolved and expressed in rectangular form. Using the shorthand notation

= 17.3 + j10 25Z-45° = 25 cos 45° - j25 sin 45° = 17.7 - j17.7

A calculator is a handy tool for resolving vectors. Many calculators have automatic programs for converting vectors from one form to another.

Now adding we obtain

where A cos 0 is the vector projection on the real axis and jA sin 0 is the vector projection on the imaginary axis, as shown in Figure III.3.

Both rectangular and polar expressions of a vector quantity are useful when performing mathematical operations.

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