Find the principal root of the complex number: (1– (2+ 4i)²

Q: Find the real and imaginary parts of the complex number. -6 + 4i

A: we have to find the real and imaginary parts of the complex number. z=-6+4i

Q: Determine the absolute value of the complex number z = -1 - 2i.

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 + 2i

A: z=-4+2i Now, r=-42+22=20=25 & θ=tan-1yx=tan-12-4=π-tan-112     ∵Given complex number lies in…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.√3 + i

A: 3+i

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 - 4i

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 - 4i

Q: For the complex number 3+ 4i the real part is and the imaginary part is

A:

Q: Represent the complex number geometrically.(-3i)(2 - i)

A: -3i2-i=-3i2-3i-i=-6i+3i2=-6i+3-1=-3-6i

Q: Extract the square root of the complex number 8-6i.

A: We have to find the square root of the complex number 8-6i.

Q: For the complex number 3 + 6i the real part is and the imaginary part is

A: Given that Complex number = 3 +6i

Q: Find the real and imaginary parts of the complex number.

A: z = a + ib                          where,  a…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.15

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.

Q: perform the indicated operations and express the answers in the standard form of a complex number.…

A: 6-3i--2+5i

Q: Represent the complex number geometrically.-2 - 6i

A: Complex numbers are defined as numbers in the form z=a+bi where ii is the imaginary part and a and b…

Q: This complex number is pure real? 1-2i/i and why?

A: For a complex number, z=x+iy, where x is the real part, y is the imaginary part. The complex number:…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.1 - i

A: Given, To Evaluate, the complex number in trigonometric form with 0 ≤ θ < 2π.1 - i Here  a=1 and…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-7

A: We know that any given complex numberz=x+iy can be written in polar form as below z=rcosθ+isinθ…

Q: What is the complex conjugate of -6 + 4i?

A: Complex number is -6+4ithen complex conjugate is -6-4i

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-5√3 - 5i

A: given the complex number -5√3 - 5i. We need to convert the following into trigonometric form.

Q: Transform the complex number into its rectangular and exponential form. (2 -5i)

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-12i

A: Consider the complex number  −12i

Q: For the complex number 3  4i the real part is ,and the imaginary part is

A: Complex number: The complex number is 3+4i For any complex number a+ib the real part is a the…

Q: Plot the complex number z = 3 + 2i and find its absolute value.

A: Consider the provided complex number, z=3+2i Find its absolute value. The absolute value of a…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-5

A: Let  z = x + iy  then  z can br written as reiθ where r = x2+y2           θ = tan-1yx

Q: Represent the complex number geometrically.-(3 - 6i)

A: Represent the complex number geometrically.-(3 - 6i)=-3+6i

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4√3 + 4i

A: Given: -4√3 + 4i Here  x=-43, y=4r=x2+y2=-432+42r=163+16=64r=8                        ... taking…

Q: Convert the complex number z = -√2 (lis (317) in its rectangular shape

A: Given: z=2cis3π4 To find: Rectangular form of given complex number.

Q: Find the real and imaginary parts of the complex number.

A: Given complex number: i3

Q: Find the quotient (2 - 3i)/(3 + 4i) , and express the result in the standard form of a complex…

A: We have given quotient 2-3i3+4i Then,…

Q: perform the indicated operations and express the answers in the standard form of a complex number.…

A: Perform the indicated operations and express the answers in the standard form of a complex number.…

Q: An engineer wants to determine the distance d of the two complex number in the complex coordinate…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Plot the complex number z = 4i and find its absolute value.

A: To plot the complex number z=4i and find its absolute value.

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.2√3 + 2i

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.1 - 3i

A: Consider the complex number: 1-3i. Write in the trigonometric form   A complex number a+ib in the…

Q: Plot the complex number z = 4 - i and find its absolute value.

A: In the Argand plane, the real axis is the x-axis and the imaginary axis is the y-axis. The absolute…

Q: Plot the complex number z = 3i and find its absolute value.

A: Plot the complex number z = 3i and find its absolute value.

Q: Find the difference of the complex numbers in the complex plane. (4 + 2i) - (5 + 4i)

A:

Q: divide the complex numbers and express your answer in form (a+bi) 3-4i/8+2i

A: The given complex number is 3-4i8+2i

Q: What is the real part of the complex number z= -1 + √3i/2

A: Compare with complex number

Q: Plot the complex number. 6V2 - 6/2i

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.4 - 3i

A: Given: z=4-3i We know that any given complex numberz=a+ib can be written in polar form as below…

Q: Find the complex conjugate of (2+3i)/(1-i)

A: We find complex conjugate of (2+3i)/(1-i)

Q: Identify the real and imaginary parts in the following complex number: -9 -12i

A: Given complex number is : -9 - 12i The real number a is called the real part of the complex number a…

Q: How many complex numbers satisfies both equations, z - i = 2 and |z– 4i| ='1?

A: z=x+iyThen,z-i=2x+iy-i=2x+iy-1=2…

Q: What is the real and imaginary parts of the complex number -5/6i

A: z = - (5/6)i can be written as, z = 0 + (-5/6)i

Q: = - z. - z.

A: We have to solve given problem:

Q: Solve 2x2 - x + 4 = 0 over the set of complex numbers.

A: Given that, 2x2-x+4=0

Q: Solve 3x2 - x + 4 = 0 over the set of complex numbers.

A: Given : 3x2 - x + 4 = 0   Use the quadratic formula to find the solutuons.   x = (-b ± √b2 - 4ac)/2a…

Q: Determine the absolute value of the complex number 2 - 3i.

A: Absolute value of complex number z=a+ib is represent by z and  given as z=a2+b2

Q: Transform the complex number into its rectangular and exponential form. (2 +2i)

A: Here, the given complex number is: z=2+2i which is of the form x+iy. So, the given complex number is…