
UNIT5-OBJECTIVE5-EXPONENTIAL FORM OF
A COMPLEX NUMBER
Another way a complex number can be represented is the exponential form of a complex number. It is called the exponential form of a complex number because it involves an exponents of a number e. (remember e2.71828------) namely
. The angle
is in radians (
). Examples 1.Write the complex number 6 (
) in exponential form. there r=6,
Since
needs to be in radians
So 6(
)=6
2.Write the complex number 8
in exponential form. Since r=8,
Convert
to radians
So 8
=8
3.Express -5-8j in exponential form.
tan
=-8/-5=1.6
(Since 5-8j is in the third quadrant) So -5-8j=9.4340
4.Express 4.6
in polar and rectangular form. (the exponent for e should be 5.7j not 5-7j) r=4.6
=5.7
Which is approximately 3.8397- 2.5332j.
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