SOLUTION: 1. Find the modulus and argument of the following complex numbers, and write them in trigonometric form:
a. 5 – 8i
b. –1 – i
c. –5 + 12i
d. 1 + √3i
2. Express each of
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-> SOLUTION: 1. Find the modulus and argument of the following complex numbers, and write them in trigonometric form:
a. 5 – 8i
b. –1 – i
c. –5 + 12i
d. 1 + √3i
2. Express each of
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Question 1117670: 1. Find the modulus and argument of the following complex numbers, and write them in trigonometric form:
a. 5 – 8i
b. –1 – i
c. –5 + 12i
d. 1 + √3i
2. Express each of the following complex numbers in the rectangular form: a + bi.
a. 2 (cos30° + i sin 30°)
b. √2 (cos135° + i sin 135°)
c. 5 cis(255°)
d. √3 cis (11π/6)
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1. Find the modulus and argument of the following complex numbers, and write them in trigonometric form:
HINT. For complex number z = a + bi the modulus |z| = r = ; argument t = with correction for a quadrant;
Trigonometric form is z = r*(cos(t) + i*sin(t)).
a. 5 – 8i Modulus = .
Argument t = .
Trigonometric form 5 - 8i = .
b. –1 – i Modulus = .
Argument t = = = (in QIII)
Trigonometric form -1-i = .
c. –5 + 12i Modulus = = = 13.
Argument t = = in QII.
Trigonometric form -5 + 12i = 13*(cost)+i*sin(t)).
d. 1 + Modulus = = 2.
Argument t = = .
Trigonometric form 1 + = .
2. Express each of the following complex numbers in the rectangular form: a + bi.
a. 2 (cos30° + i sin 30°) = = .
b. √2 (cos135° + i sin 135°) = = -1 + i.
c. 5 cis(255°) = = .
d. √3 cis (11π/6) = = = = 1.5 - 0.5*i.
