Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Chapter A5.4, Problem 7P

Express the result of each of these complex-number manipulations in polar form, using six significant figures just for the pure joy of calculating (a) Chapter A5.4, Problem 7P, Express the result of each of these complex-number manipulations in polar form, using six , example  1; (b) Chapter A5.4, Problem 7P, Express the result of each of these complex-number manipulations in polar form, using six , example  2Chapter A5.4, Problem 7P, Express the result of each of these complex-number manipulations in polar form, using six , example  3; (c) Chapter A5.4, Problem 7P, Express the result of each of these complex-number manipulations in polar form, using six , example  4.

(a)

Expert Solution
Check Mark
To determine

The polar form of the given complex number.

Answer to Problem 7P

The polar form of the given complex number is 4.6917913.2183°.

Explanation of Solution

Given data:

The given complex number F is [2(141°)]0.341°.

Calculation:

The polar form of the function is given as,

B+jC=B2+C2tan1(CB)        (1)

Here,

B and C are constants.

The rectangular form of any function given in the form of Aθ is given as,

Aθ=Acosθ+jAsinθ        (2)

Here,

A is constant.

θ is the angle.

Substitute 5 for A and 41° for θ in equation (2).

141°=(1)cos(41°)+j(1)sin(41°)=0.754709j0.656059

Substitute 0.754709j0.656059 for 141° in the given complex number.

F=[20.754709+j0.656059]0.341°

F=1.24529+j0.6560590.341°        (3)

Substitute 1.24529 for B and 0.656059 for C in equation (1).

1.24529+j0.656059=1.245292+0.6560592tan1(0.6560591.24529)=1.4075327.7817°

Substitute 1.4075327.7817° for 1.24529+j0.656059 in equation (3).

F=1.4075327.7817°0.341°=4.6917713.2183°

Conclusion:

Therefore, the polar form of the given complex number is 4.6917713.2183°.

(b)

Expert Solution
Check Mark
To determine

The polar form of the given complex number.

Answer to Problem 7P

The polar form of the given complex number is 6.3183370.4626°.

Explanation of Solution

Given data:

The given complex number F is 502.8783.6°+5.1663.2°.

Calculation:

Substitute 2.87 for A and 83.6° for θ in equation (2).

2.8783.6°=(2.87)cos(83.6°)+j(2.87)sin(83.6°)=0.319915+j2.85211

Substitute 5.16 for A and 63.2° for θ in equation (2).

5.1663.2°=(5.16)cos(63.2°)+j(5.16)sin(63.2°)=2.32652+j4.60574

Substitute 0.319915j2.85211 for 2.8783.6° and 2.32652j4.60574 for 5.1663.2° in the given complex number.

F=500.319915+j2.85211+2.32652+j4.60574

F=502.64643+j7.45785        (4)

Substitute 2.64643 for B and 7.45785 for C in equation (1).

2.64643+j7.45785=(2.64643)2+(7.45785)2tan1(7.457852.64643)=7.9134870.4626°

Substitute 7.9134870.4626° for 2.64643+j7.45785 in equation (4).

F=507.9134870.4626°=6.3183370.4626°

Conclusion:

Therefore, the polar form of the given complex number is 6.3183370.4626°.

(c)

Expert Solution
Check Mark
To determine

The polar form of the given complex number.

Answer to Problem 7P

The polar form of the given complex number is 11.506654.5969°.

Explanation of Solution

Given data:

The given complex number F is 418°675°+528°.

Calculation:

Substitute 4 for A and 18° for θ in equation (2).

418°=(4)cos(18°)+j(4)sin(18°)=3.80423+j1.23605

Substitute 6 for A and 75° for θ in equation (2).

675°=(6)cos(75°)+j(6)sin(75°)=1.55291+j5.79555

Substitute 5 for A and 28° for θ in equation (2).

528°=(5)cos(28°)+j(5)sin(28°)=4.41474+j2.34736

Substitute 3.80423+j1.23605 for 418° and 1.55291+j5.79555 for 675° and 4.41474+j2.34736 for 5.1663.2° in the given complex number.

F=3.80423+j1.236051.55291+j5.79555+4.41474+j2.34736=6.66606+j9.37898

Substitute 6.66606 for B and 9.37898 for C in equation (1).

6.66606+j9.37898=(6.66606)2+(9.37898)2tan1(9.378986.66606)=11.506654.5969°

Conclusion:

Therefore, the polar form of the given complex number is 11.506654.5969°.

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