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3 years ago

Given z=4+3i evaluate z

Mathematics

1 answer:

DerKrebs [107]3 years ago

5 0

Answer:

Step-by-step explanation:

Assuming we want to evaluate |z|, given that, z=4+3i.

Then, by definition of modulus,

$|x + yi| = \sqrt{ {x}^{2} + {y}^{2} }$

$|4+ 3i| = \sqrt{ {4}^{2} + {3}^{2} }$

$|4+ 3i| = \sqrt{ 16+ 9 } \\ |4+ 3i| = \sqrt{25 } \\ |4+ 3i| = 5$

Therefore the modulus be of the given complex number is 5 units

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Suppose that theta is an angle in standard position whose terminal side Intersects the unit circle at (-11/61, -60/61)

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Answer:

The exact values of the tangent, secant and cosine of angle theta are, respectively:

$\cos \theta = -\frac{11}{61}$

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$\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}$

Step-by-step explanation:

The components of the unit vector are $x = -\frac{11}{61}$ and $y = -\frac{60}{61}$ . Since $r = 1$ , then $x = \cos \theta$ and $y = \sin \theta$ . By Trigonometry, tangent and secant can be calculated by the following expressions:

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Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:

$\cos \theta = -\frac{11}{61}$

$\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}$

$\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}$

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3 years ago

Given z=4+3i evaluate z​

Given z=4+3i evaluate z