Find all the complex roots. Write the answer in exponential form. The complex fourth roots of 10- 10 3 i.

Q: (c) Find the 3 distinct roots of 2³-2-2√√3i

A:

Q: Find the 4 fourth roots of -8+8i(square root of 3)

A: Let, z=-8+83i Since, nth root of any complex number w is defined as, wn=rncosθ+2kπn+isinθ+2kπn

Q: Find all complex roots of the equation z6+z5+z4+z3+z2+z+1=0.

A: The given equation is z6+z5+z4+z3+z2+z+1=0    .....(1) We know that  z7-1=(z-1)(z6+z5+z4+z3+z2+z+1)…

Q: find the cube roots of 125i (all of them)

A: The given complex number is z = 125i

Q: Find the nth roots of a if n = 4 and a = 10,000?

A: I'm providing hand written solution for better understanding.

Q: Find the two square roots of the number 16

A: We have to find square root

Q: Use DeMoivre’s Theorem to find all the cube roots of 2i. Show your work.

A: From the given z=0+2i. That is, a=1 and b=2. Recall the DeMoivre’s Theorem: "If Z=rcosθ+isinθ, then…

Q: show all the work please asap

A: Roots:            Polar form:…

Q: The fifth roots of 1 are

A: We have to find the fifth root of 1. Let z=15 ⇒z5=1 We know that e2kπi=1 for every k∈Z. Hence,…

Q: Find and graph all specified roots of 1:

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find and graph all specified roots of i. third(cube)

A: Given : z = i     ......(1)   where, z = a+ib     ....(2)            comparing equation (1) and (2).…