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Find the trigonometric form of a complex numberThe algebraic form of the complex number...
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You need to convert the algebraic form `z = 1 + i` into trigonometric form, such that:
`z = sqrt(1^2 + 1^2)(cos (tan^(-1)(1/1)) + i*sin (tan^(-1)(1/1)))`
Replacing `45^o` for `(tan^(-1)(1/1))` yields:
`z = sqrt 2*(cos 45^o + i*sin 45^o)`
Hence, performing the conversion from the algebraic form `z = 1 + i` into trigonometric form yields `z = sqrt 2*(cos 45^o + i*sin 45^o).`
Posted by sciencesolve on April 30, 2013 at 5:57 PM (Answer #3)
The algebraic 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|
We'll identify x and y for te given complex number:
x = Re(z) = 1
y = Im(z) = 1 (coefficient of i)
|z| = sqrt(1^2 + 1^2)
cos a = 1/sqrt2
cos a = sqrt2/2
sin a = 1/sqrt2
sin a = sqrt2/2
sin a = cos a = sqrt2/2
a = pi/4 = 45 degrees
The trigonometric form of the complex number z is:
z = sqrt2*(cos pi/4 + i*sin pi/4)
Posted by giorgiana1976 on June 4, 2011 at 4:22 AM (Answer #2)
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