Determine real part, imaginary part and absolute value of the following complex numbers: b) 3e −9iπ/4 ;

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

A: z=-2-7i Now, r=-22+-72=53 & θ=tan-1yx=tan-1-7-2=π+tan-172      ∵The given complex number lies in…

Q: Find the value of real number if the complex number is 8 + 9j = 0

A: Given complex number is 8+9j=0 Real value of the given complex number is 8. Real number can be…

Q: What happens when a complex number is multiplied by its conjugate? It turns into a real number…

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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.-4 - 4i

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

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-10 + 10i

A: We have given  z = -10 + 10i    Now, z can written as reiθ    r =  (-10)2+ 102              [ As if…

Q: Find the square roots of the given complex number by using result (10) and then confirm the result…

A: Given:  1) 2-3i2) -2-i Find the square roots of the given complex number by using result (10) and…

Q: How would I find the magnitude of the complex number based on the given values for z?

A: To find the magnitude of the complex number

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: 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: Find all complex numbers z satisfying z³ = 27i and give your answer as a comma-separated list of…

A: We have to find Z value

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: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given that, 2+23i10

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

A: Consider the complex number  −12i

Q: Solve over the set of complex numbers. x +32 0 2x2 -10 = -50 17. 18. 19. 3x2 =-12 %3D

A: We have to solve

Q: Evaluate (3−4i)(8i) and express as a simplified complex number.

A: A complex number is of the form z = x + iy. where x is real part of z and y is imaginary part of z.…

Q: Determine the absolute value of the complex number z = 3 + 4i

A: Given: z=3+4i

Q: Find the conjugate, argument and modulus of the complex number Z=1+i3

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Q: Pick two complex numbers (like a + bi and c + di) and consider if the following statement is True or…

A: Set of pure imaginary numbers

Q: In the complex number system, what is the value of the expression 16i* – 8i? + 4 ? (Note: i = -1)

A: Substitute the value of i and simplify the results.

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given :            -22 + 22i15   To change the given complex number to the form a + bi using De…

Q: If z is a complex number, show that the sum of z and its conjugate is a real number.

A: Given z is a complex number. Let z=x+iy We know that conjugate of a complex number is given by…

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: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given: Let z=1-3i3 To Find: To change the given complex number into a+ib form using De Moivre’s…

Q: Evaluate b. Topic under Cartesian Complex Numbers

A: Given, -1j7

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

A: Given complex number: i3

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-20i

A: -20i

Q: Use de Moivre's formula to find the Cartesian form of the complex number (-1+iv3) *".

A: The given complex number is                                      -1+i3-7 De Moivre's formula:…

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

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: . Ifa complex number z has modulus 2 and argument , then

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Q: 1. Write the complex number 2 + iv3 in the form of rei0

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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: Let z = 3 – Ai, w = 1+ 2i be complex numbers. For both z and w, what is the: • Real part • Imaginary…

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Q: The variable z is often used to denote a complex number and 7 is used to denote its conjugate. If z…

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

A: 12+0i

Q: To divide two complex numbers in trigonometric form, ________ their moduli and_____ their arguments.

A: If z1=r1cosθ1+isinθ1=r1cisθ1 andz2=r2cosθ2+isinθ2=r2cisθ2 are two complex numbers intrigonometric…

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: Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are…

A:

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

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

Q: Find the square roots of the given complex number by using result (10) and then confirm the result…

A: We can find the square root of complex number by using the formula.

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

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.3 - 3√3i = 3 (1 - √3i) Multiply…

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Solution: Consider the given complex number is: z = 3 + i7 We have  z = a + ib⇒z = rcos θ + i sin θ…

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given complex number is: Let us consider, r cos θ=22r sin θ=-22 Then we get,…

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: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given complex number is: 22+22i25 Let us consider, r cos θ=22r sin θ=22 Then we get,…

Q: What is the first step in writing the complex number -1 + i in trigonomet-ric form?

A: Consider z=x+iy is any complex number, so polar form is, z=x+iy=rcosθ+isinθWherer=x2+y2θ=π-tan-1yx…

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

A: Here the given complex number z=x+iy=3+2i⇒x=3,⇒y=2

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