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Complex numbers.Write the trigonometric form of the complex number z = 3 + 4i.
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We'll write the rectangular form of any complex number is z = x + y*i.
The trigonometric form of a complex number is:
z = |z|(cos a + i*sin a)
|z| = sqrt(x^2 + y^2)
cos a = x/|z|
sin a = y/|z|
Comparing, we'll identify x and y for the given complex number:
x = Re(z) = 3
y = Im(z) = 4 (only the coefficient of i)
|z| = sqrt(3^2 + 4^2) => |z| = sqrt(9 + 16) => |z| = sqrt25 => |z| = 5
cos a = 3/5
sin a = 4/5
tan a = y/x
tan a = 4/3
a = arctan (4/3)
The trigonometric form of the complex number z is:
z = 5*[cos (arctan (4/3)) + i*sin (arctan (4/3))]
Posted by giorgiana1976 on May 24, 2011 at 4:37 PM (Answer #2)
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