Chapter 2: Q16P (page 74)

Evaluate each of the following in x+ iyform, and compare with a computer solution.
${(\frac{1 + i \sqrt{3}}{2})}^{'}$

Short Answer

Expert verified

The value of $(\frac{1 + i \sqrt{3}}{2})$ is Where $n = 0, 1, 2, 3 . .$ .

Step by step solution

Given Information.

The given expression is ${(\frac{1 + i \sqrt{3}}{2})}^{'}$ .

Definition of Complex Number.

The numbers that are presented in the form of $x + i y$ where, $' x, y'$ are real numbers and $' i'$ is an imaginary number, those numbers are referred to as called Complex numbers.

Find the value of (1+i32)'.

Let the complex numbers as:

$u = {(\frac{1 + i \sqrt{3}}{2})}^{'} z = \frac{1 + i \sqrt{3}}{2}$

Find the modulus of the complex number.

$r = |z| = 1$ .

Find the argument of the complex number.

$θ = \frac{π}{3} u = e^{(In {(z)}^{i})} e^{(I n (z) i)} = e^{(i [In (r) + i (θ + 2 n π)])} = e^{[i (I n (1) + i (\frac{π}{3} + 2 n π))]} = e^{[- (\frac{π}{3} + 2 n π)]} n = 0, 1, 2, 3, . . .$

Hence the value of ${(\frac{1 + i \sqrt{3}}{2})}^{'}$ is $e^{[(- \frac{π}{3} + 2 nπ)]}$ Where role="math" localid="1658815979004" $n = 0, 1, 2, 3, . .$

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Evaluate each of the following in x+ iyform, and compare with a computer solution.
${(\frac{1 + i \sqrt{3}}{2})}^{'}$

Short Answer

Step by step solution

Given Information.

Definition of Complex Number.

Find the value of (1+i32)'.

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Evaluate each of the following in x+ iyform, and compare with a computer solution.(1+i32)'

Short Answer

Step by step solution

Given Information.

Definition of Complex Number.

Find the value of (1+i32)'.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Wave Optics

Medical Physics

Electric Charge Field and Potential

Thermodynamics

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

Evaluate each of the following in x+ iyform, and compare with a computer solution.
${(\frac{1 + i \sqrt{3}}{2})}^{'}$