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Solved Examples
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eee Find the indicated power of [7(cosθ2-i sinθ2)]14.
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eee Find (cos θ + i sin θ)7.
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eee Evaluate [8(cos 30° + i sin 30°)]2. eee View Solution
eee Simplify [8(cos 20° + i sin 20°)]6. eee View Solution
eee Simplify 4(cos 3θ - i sin 3θ)7.
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eee Simplify:
(cos 10π13 - i sin 10π13)13
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eee Change the rectangular coordinates P (3, - 4) to polar coordinates.
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eee Change the rectangular coordinates P (0, 5) to polar coordinates.
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eee Find (cos θ + i sin θ)3.
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eee Evaluate [4(cos 30° + i sin 30°)]2. eee View Solution
eee Simplify [6(cos 20° + i sin 20°)]6. eee View Solution
eee Simplify 3(cos 5θ + i sin 5θ)8.
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eee Simplify:
(cos 4π7 + i sin 4π7)7
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eee Using De Moivre's theorem, write (1 - i)4 in the form of a + ib. eee View Solution
eee Using De Moivre's theorem, express (3 + i)6 in the standard form a + i b.
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eee Simplify:
(- 2 + i)5
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eee Find the indicated power of the complex number in standard form a + ib.
(12+32 i)12  eee
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eee Find the indicated power of [5(cosθ2-i sinθ2)]10.
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eee Simplify:
(cos 30o - i sin 30o)7
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eee Simplify:
cos 3θ + i sin 3θcos θ + i sin θ
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eee Simplify:
(cos 2θ + i sin 2θ)3(cos 3θ + i sin 3θ)2
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eee Find the indicated power of [3(cos 10°+ i sin 10°)]9. eee View Solution
eee Change the rectangular coordinates A (2, 3) to polar coordinates.
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eee (2cosπ12+2i sinπ12)8 = eee View Solution
eee (cosπ5 + i sinπ5)20 = eee View Solution
eee Use De Moivre's theorem to express (1 + i)10 in the standard form a + ib. eee View Solution
eee Find (1 - 2i)8 using De Moivre's theorem.  eee View Solution
eee Find [1 - i2]5 using De Moivre's theorem.
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eee If Z = 3(cos π4 + i sin π4) and W = 2(cos π2 + i sin π2), then find ZW . eee View Solution
eee Change the polar coordinates P(4, 45°) to rectangular coordinates.
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eee If Z = 2(cos 4θ + i sin 4θ) and W = (cos θ2 + i sin θ2), then find ZW.
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eee Change the polar coordinates P (- 4, 60°) to rectangular coordinates. eee View Solution
eee If Z1 =3 + i and Z2 = 1 + i, then find the product of Z1Z2. eee View Solution
eee Change the polar coordinates A (6, 150°) to rectangular coordinates.
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eee Change the polar coordinates B (8, - 330°) to rectangular coordinates. eee View Solution
eee If Z1 = 8[cos π2 + i sin π2] and Z2 = 2[cos π4 + i sin π4], then find the value of z1z2. eee View Solution
eee Simplify:
(cos θ+ i sin θ)6cos 3θ+i sin 3θ eee
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eee If Z1 = 2(cos 3θ+i sin 3θ) and Z2 = 12(cos θ+i sin θ), then find the value of Z1Z2. eee View Solution
eee Find the cube roots of (1 + i).
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eee Change the polar coordinates P (- 3, 240°) to rectangular coordinates. eee View Solution
eee Find the cube roots of - 27. eee View Solution
eee Express in polar form: 2 - 3i eee View Solution
eee Find the fourth roots of 81(cos 240o + i sin 240o).
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eee Express the complex number - 5 + 5i in polar form.
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eee Express in polar form: -1 eee View Solution
eee Express the complex number 3i in polar form.
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eee Express the complex number 2 + i in polar form.
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eee Express the complex number - 3 + 2i in polar form.
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eee Find the fourth roots of 2 - 23i.
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eee Express in polar form 12 + (32)i.
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eee Express in standard form (cos 60° + i sin 60°).
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eee Express - 2(cos 150° + i sin 150°) in standard form.
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eee Express cos 10° + i sin 10° in standard form.
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eee Express 0.3(cos 174° + i sin 174°) in standard form.
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eee Express 2[cos (- 60°) + i sin (- 60°)] in standard form. eee View Solution
eee Change the rectangular coordinates B (- 3, 1) to polar coordinates.
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eee Change the rectangular coordinates Q (- 3, 0) to polar coordinates.
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eee Change the polar coordinates Q (- 3, - 270°) to rectangular coordinates. eee View Solution
eee If n is a positive integer, then find the value of (1+ cos α + i sin α)n.
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eee If 2cos θ = a + 1a and 2cos j = b + 1b, then find the value of cos (θ - j). eee View Solution
eee Given that |z| = 4 and arg z = 5π6 then z = ________
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eee Express in polar form the roots of x5 - 32 = 0 which when graphed would be a vector in the second quadrant.
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eee If x + 1x = 2cos π18, then find the value of x9+1x9.
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eee Change the rectangular coordinates A (- 5, - 53) to polar coordinates.
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eee What is the argument of the complex number 2 - i2? eee View Solution