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Problem 41
In Exercises 37–52, perform the indicated operations and write the result in standard form. __ (−2 + √−4)²
Problem 43
In Exercises 37–52, perform the indicated operations and write the result in standard form. __ (−3 − √−7)²
Problem 45
In Exercises 37–52, perform the indicated operations and write the result in standard form. ___ −8 + √−32 / 24
Problem 1
In Exercises 1–10, plot each complex number and find its absolute value. z = 4i
Problem 5.2.45
In Exercises 45–52, find the quotient z₁/z₂ of the complex numbers. Leave answers in polar form. In Exercises 49–50, express the argument as an angle between 0° and 360°.
z₁ = 20(cos 75° + i sin 75°)
z₂ = 4(cos 25° + i sin 25°)
Problem 5.2.56
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 40° + i sin 40°)]³
Problem 5.2.63
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (√3 − i)⁶
Problem 5.2.60
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [√3 (cos (5π/18) + i sin (5π/18))]⁶
Problem 5.2.53
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [4(cos 15° + i sin 15°)]³
Problem 5
In Exercises 1–10, plot each complex number and find its absolute value. z = 3 + 2i
Problem 5.2.65
In Exercises 65–68, find all the complex roots. Write roots in polar form with θ in degrees. The complex square roots of 9(cos 30° + i sin 30°)
Problem 5.2.55
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 80° + i sin 80°)]³
Problem 5.2.58
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [1/2 (cos π/10 + i sin π/10)]⁵
Problem 5.2.61
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (1 + i)⁵
Problem 5.2.57
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [1/2 (cos π/12 + i sin π/12)]⁶
Problem 5.2.49
In Exercises 45–52, find the quotient z₁/z₂ of the complex numbers. Leave answers in polar form. In Exercises 49–50, express the argument as an angle between 0° and 360°.
z₁ = cos 80° + i sin 80°
z₂ = cos 200° + i sin 200°
Problem 5.2.64
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (√2 − i)⁴
Problem 5.2.62
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. (1 − i)⁵
Problem 5.2.59
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [√2 (cos (5π/6) + i sin (5π/6))]⁴
Problem 5.2.54
In Exercises 53–64, use DeMoivre's Theorem to find the indicated power of the complex number. Write answers in rectangular form. [2(cos 10° + i sin 10°)]³
Problem 9
Plot each complex number and find its absolute value. z = −3 + 4i
Problem 11
Plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. 2 + 2i
Problem 15
In Exercises 11–26, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. −4i
Problem 19
In Exercises 11–26, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. −3
Problem 23
In Exercises 11–26, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. −3 + 4i
Problem 27
In Exercises 27–36, write each complex number in rectangular form. If necessary, round to the nearest tenth. 6(cos 30° + i sin 30°)
Problem 31
In Exercises 27–36, write each complex number in rectangular form. If necessary, round to the nearest tenth. 8(cos 7π/4 + i sin 7π/4)
Problem 35
In Exercises 27–36, write each complex number in rectangular form. If necessary, round to the nearest tenth. 20(cos 205° + i sin 205°)
Problem 37
In Exercises 37–44, find the product of the complex numbers. Leave answers in polar form. z₁ = 6(cos 20° + i sin 20°) z₂ = 5(cos 50° + i sin 50°)
Problem 41
In Exercises 37–44, find the product of the complex numbers. Leave answers in polar form. z₁ = cos π/4 + i sin π/4 z₂ = cos π/3 + i sin π/3