1. Find all the third roots of i and plot them on the Argand diagram.

Q: a) Use DeMoivre's theorem to find all roots of: w3 = Z = -27 in the complex plane.

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Q: Let the complex numbers z₁,z2 and z3 be the vertices of an equilateral triangle. If zo is the…

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Q: 1. Consider the equation (2¹ +64) = 32√√3³. Find all the roots and express them in rectangular form.…

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Q: 2) Consider complex numbers z₁ = 4-3i and z₂ = −6+4i and compute a. Z₁ Z₂ b. 21 Zz C. Z1

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Q: 1. Find the cube roots of −1+√3i then represent each root in the argand plane

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Q: Find the length of the line given by r(t) = (9t,10t) for astsb. The length of the line is (Type an…

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Q: Which of the following graphs represents i(4+31) in the complex plane? B

A: Given -  Complex Number To Find - Plot on Argand Plane

Q: V-12 V-40 V-72

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Q: A car safety association conducted tests to measure the stopping distances of a new model of car and…

A: solution:  Straight relapse is a direct way to deal with model the connection between a reliant…

Q: Let z, and z2 be two complex roots of the equation z2 + az + b = 0. Assume that the Origin, z1, and…

A: Given  Let z₁ and z₂ be two complex roots of the equation                  z² + az + b = 0. Assume…

Q: Find all the fifth roots of 1 + i√3

A: That's easy.

Q: (IV) Solve and sketch the solutions (in the Gauss plane) for the following roots: 327, 3-8, Vi

A: Let z3=27z3=33z3−33=0(z−3)(z2+3z+32)=0Then z−3=0⇒ z=3and z2+3z+9=0⇒ z=−3±9−362⇒ z=−3±33 i2Thus the…

Q: Sketch each of the following sets of complex numbers z that satisfy the given equations/inequalities…

A: We will use basic Complex analysis

Q: 3.] Find the polasz form of the complex number √3 +i Z

A: Given that the complex number is  z= √3 + i  We have to calculate the polar form of this complex…

Q: Find (approximate in standard form) & graph the 8th roots of z=-6401 +1440i Show your work for zo…

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Q: Find the rectangular and Euler form (1+2i)² of -12+9i

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Q: If a and b are complex numbers, prove that |a+b|<\a|+\b| .

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Q: Given two complex numbers z and w such that z = (1+ i)w + (3 –- i)w, where w is the conjugate of w.…

A: z and w are two complex numbers. Such that

Q: Qi Find the Complex roots For

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Q: :If z is a complex number satisfying the equation (-1)" = =", where n e N. Show that the locus of z…

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Q: Compute and graph all the roots in the complex plane following the format.   a. the value of x and…

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Q: 5. Determine all roots of the equation z4 – 9 = 0, and sketch them on the complex plane.

A: Given equation:                            z4-9=0

Q: Draw/Describe the set of points in the complex plane that satisfies |2z – i| = 4.

A: Let the complex number,  z=x+iy . The expression, |z| is calculated using the formula, |z|=x2+y2 .

Q: Let the complex numbers z₁,z₂ and z3 be the vertices of an equilateral triangle. If zo is the…

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