determine z and |z| for the given complex number.

Q: Find the polar form for the complex number -2-3i.

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Q: Multiply each complex number by its complex conjugate. a. 3 + 6i   b. 2 − 5i

A: A complex number is a number of the form a+bi with a,b being real numbers. In this form we have a is…

Q: Plot each of the given complex numbers in an Argand diagram and label all the necessary parts. Also,…

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Q: Consider the complex number z = (1 – i)(-1-iv3). Find |2| and arg(2).

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Q: b) Write the following complex number in Cartesian, Polar and Exponential for VZ+ Või -1+ v3i

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the roots of the given complex number 1. z^3 = 2 – 3i

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Q: Use the trigonometric form of a complex number to show that z-n = 1/zn , where n is a positive…

A: To prove the given identity

Q: bi is raised to m if Find the imaginary component if the complex number a + a = 6, b = 6, and m = 7.

A: We have to find the imaginary component if the complex number a+ib is raised to m if a=6, b=6, and…

Q: Find the radius  and angle of each complex number.  Z=4-3i Z=2+3i Z=3 Z=1+i Z=8+i

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Q: ind the roots of complex numbers 1. z3 = 2 – 3i

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Q: Plot each of the given complex numbers in an Argand diagram and label all the necessary parts. Also,…

A: Since there are multiple questions the first question is answered as per our guidelines. Kindly…

Q: (7-21) and (5 + 8i)

A: Find the distance between and the midpoint of each pair of complex number (7-2i) and (5+8i) .

Q: find each of the products and express the answers in the standard form of a complex number. (4 + 5i…

A: Consider the given complex number. C=(4+5i)2 The algebraic formula is defined as, a+b2=a2+b2+2ab

Q: Find the fifth roots of the complex number 3 - 4i

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Q: Represent the complex number geometrically.4(-1 + 2i)

A: 4-1+2i

Q: (a) Find all the complex roots of (7+6i)/3

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Q: Write the complex number in polar form with argument 6 between 0 and 2n. 9 + 9/3i

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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: find the square of the complex number 2 -2i and write the answer in a form a + bi where as a and b…

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Q: 2. Identify the conjugate of each complex number, then plot both complex numbers and their…

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Q: Write the complex number in polar form with argument e between 0 and 2n.

A: Given: z=2z=2+0i

Q: Put the complex number of (1+2i)/(2+i) in the form if a +bi, where a and b are real numbers

A: The given complex number is 1+2i2+i.

Q: Find all the complex roots of (4 – 4i)1.

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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: Evaluate (3+5i)(−2−2i)and express as a simplified complex number.

A: We have to evaluate (3+5i)(−2−2i)

Q: Find the imaginary component if the complex number a + bi is raised to m if a = 7, b = 7, and m = 6.

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

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Q: Find the roots of the given complex number 1. z^5 = 4i

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Q: Take the last four digits ABCD of your student identification number, and let z1 = A + Bi and z2 = C…

A: We will be taking the last 4 digits as ABCD. Let z1 = A + Bi and z2 = C + Di be the corresponding…

Q: Given the complex number z such that z-4i = a+3zi , find the value of a if z is purely imaginary.

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Q: The value √(a2 + b2) is the_______ of the complex number a + bi.

A: Solution:-  The value a2+b2 is the_______ of the complex number a + bi

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: Find a complex number so that c^2=i

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Q: .z³ = 8i

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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: Z is a complex number

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Q: FIND THE ARG CZ) OF THE COMPLEX NUMBERS 2

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Q: Find all complex numbers z E C that satisfy the equation (7) + 3 = 0.

A: Solve the following

Q: Find the four fourth roots for the complex number: v2 + v2i

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Q: Find the following products of complex number (2 - i)(-2 - 3i)

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Q: Z = (1 - j)¹-2j

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Q: Write the following complex number in Polar form: 5+ V4i Z= 5-6i

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Q: 7. Plot the complex number 3 - 6i

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Q: Write the complex number in polar form with argument e between 0 and 2n. -8i

A: The polar form is  8(cos(3π/2) + i sin(3π/2))

Q: Add the two complex numbers: (3 + 4i) + (5i).

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

A: Concept  -If a complex number is given as - z = a+biThen,a = real partb = imaginary part

Q: If the complex number z and its conjugate z' satisfy zz' + 2(z - z') = 12 + 8i, then the values of z…

A: Explanation of the answer is as follows