a) Compute the four 4th roots of −T + Ti

Q: Find the four fourth roots of -1 -√3 i.

A: Given, z=-1-3i

Q: Find the three cube roots of -8i.

A:

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: 4-3i4+3iRationalise the…

Q: Find all the 6 roots of -i

A:

Q: Find the three cube roots of 1.

A:

Q: ) Prove that sum of all cube roots of unity is zero.

A:

Q: Determine all the roots of z +1 = 0

A: The given question is related with complex analysis. We have to determine all the roots of z4 + 1 =…

Q: Perform the computations in the given question and express the results in standard form a+ bi.   i15

A: The given expression is i15.

Q: Find the distinct roots of (-1 – 3j)°/7

A: Given: The objective is to find the distinct roots of -1-3j37.

Q: - Find the three cube roots of 27i.

A:

Q: 1. Find the primitive roots (if they exist) of: (а) 40 (b) 50 (с) 71

A:

Q: Find the four roots of ( 3 + 14 )

A: To find the four roots of the complex number.

Q: Show that -1+ /3i is a cube root of 1 (meaning that its cube equals 1).

A: Find the cube of the expression and prove that it is equal to 1

Q: Find the four roots of ( 3+14)

A: The given problem is related with complex analysis. We have to find the four roots of 3 + i4. Note…

Q: Find all the distinct 5th roots of 32, then plot the results on an Argand diagram.

A:

Q: find the three cube roots of 8 . Express the roots in rectangular form .

A: 8=2x2x2

Q: Find the three roots of 8.

A:

Q: Find the 99th roots of 12-13i

A:

Q: Find the distinct roots of (-7 + 2j)3/4.

A: We know that, 1.Let z =rcosθ +isinθ    then zn =rncosnθ +isinnθ 2. A number u is said to be an n-th…

Q: Find the 6 roots of -i

A: We have given that ,  z = -i We need to find sixth roots of z = -i. First we will find polar form of…

Q: Find the 2 square roots of 3 - 4j using De Moivre’s Theorem.

A: The given complex number isz=3-4jto find z12

Q: Perform the computations in the given question and express the results in standard form a+ bi.   (2…

A: Given: 2-3i-1+4i Simplify the expression: 2-3i-1+4i=2-1+4i-3i-1+4i=-2+8i+3i-12i2=-2+11i-12i2

Q: 15. Find the two square roots of the following and write your answer in standard form. 2+ 2iv3

A:

Q: Perform the computations in the given question and express the results in standard form a+ bi.   (2…

A: Given: 2-i3 Simplify using the identity (a-b)3=a3-b3-3ab(a-b). 2-i3=23-i3-3(2)(i)(2-i)

Q: Find three (3) distinct roots of the cuberoot of 8 and express the root in rectangular form.

A:

Q: Calculate all the primitive roots of 41 and 26.

A: (a) Consider a=41. Therefore: φa=φ41=411-410=40 Now φa=40 can be written as: φa=40=23×5. Therefore…

Q: a) Calculate the 4th roots of (5-j3)

A: The objective is to calculate the 4th roots of (5-j 3).

Q: Find the roots of (-i +1) all to the power 1/3

A: Our objective is to find the roots of (-i +1) all to the power 1/3

Q: Find the four roots of the number 16- as a result of the assumption

A: To find fourth root of 16 by asumption. Let x=164

Q: Prove that sum of all cube roots of unity is zero.

A: First we prove that the sum of all the distinct nth roots of unity is zero.

Q: Apply the nth root theorem to find all the roots of x3 + (2/3-2i)-0

A:

Q: Find the 9 9th roots of 12-13i

A: 12-13i = re-iθr=122+132=313θ=tan-11312=-47.28

Q: Find the 5 fifth roots of -4+5i.

A:

Q: Find the 4 4th roots of 4+10i

A: Given: z = 4 + 10i

Q: (b) Let A₁, A2, · · ·, №46 be the roots of 2¹ 1/46 that 46 Σλ = 0 i=1 . Show

A:

Q: 1. Determine the four roots of z = -2 + 2i.

A: Given;  z = -2+2i. Repost the 2nd question.

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: We have the given rational expression for complex number as 1-i1+3i On multiplying both numerator…

Q: Find the three cube roots of 1

A: let x be he cube root of 1 x=13 therefore x3-1=0 use the formula a3-b3=a-ba2+b2+ab x3-13=x-1x2+12+x…

Q: Find the three cube roots of -27i.

A: Find the three cube roots of -27i. We can split the number as 3 * 3 * 3 * i * i * i Applying Cube…

Q: 8. Sketch the roots of 28 =-16

A: This is a problem of complex analysis. The objective is to sketch the roots of z8=-16.

Q: 2. Compute each set of roots and provide the results in Cartesian form a) x5 = a = -1

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: Perform the computations in the given question and express the results in standard form a+ bi. 1/2-i

A: z=12-irationalise the denominator z=12-i×2+i2+iz=1(2+i)(2-i)(2+i)using the identity…

Q: Perform the computations in the given question and express the results in standard form a+ bi. (5 -…

A: The standard form is  a+biSo,(5−3i)(2−4i)=10−8i-6i+12i2

Q: Find the three cube roots of  z= -2 + i

A: Given The given complex number is z=-2+i. Use De Moivre's theorem for nth root of complex number…

Q: 3. Determine the cube roots of 8 at 120 degrees.

A: We have to determine the cube roots of 8 at 120 degrees. We will convert it to polar form and use…

Q: The n distinct nth roots of 1 are called the nth roots of ________.

A: The n distinct nth roots of 1 are called the nth roots of unity .

Q: calculate all the fourth roots of 2 cis (pi/4)

A:

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: The given complex expression is, 5+2i5-2i The objective is to write the expression in standard form…

Q: 2. Find all the 6th roots of 32-32√3i.

A:

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: 13+i=13+i×3-i3-i=3-i32-i2

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.