Find all complex numbers z such that z2=-5+12i, and give your answer in the form a+bi. Use the square root symbol 'V' where needed to give an exact value for your answer.

Q: Find all complex fourth roots of -2-2/3 i. In other words, find all complex solutions of x = =…

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

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Q: Find all the complex numbers x that satisfy the equation x5 - ix4 + 5x3-5ix2 + 6x - 6i = 0. Then…

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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: Need help

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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: Write the complex number in polar form with argument 0 between 0 and 2x.

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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 all complex square roots of i. In other words, find all complex solutions of x i

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Q: Cannot solve

A: First we solve the equation for x

Q: 2+7i 3-3i

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Q: Write the complex number -V3 + i in trigonometric (or polar form) with 0 < 0 < 2n.

A: Using z= r(cos theta +i sin theta)

Q: Find the product of the given complex number and it's conjugate  4-7i

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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: The complex number Z1and Z2 are given by, Z1 = 3 – 5i and Z2 = -1+ 4i Determine: 2Z1 +5Z2

A: We have to determine 2Z1+5Z2 for the given complex numbers: Z1=3-5i and Z2=-1+4i Finding 2Z1:…

Q: −j j sin² zdz

A: Consider I=∫-jjsin2zdz

Q: Find all complex numbers that are solutions of the given equation. Leave your answers in standard…

A: Consider the equation : z3+8i=0. Find the solutions of the given equation. z3+8i=0z3-8i3=0…

Q: Use DeMoivre’s theorem to find (–√3/2 +i/2)12. Express your answer in complex form.

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

A: Given: z=3+4i

Q: Express the complex number z = 10 cis 315° in rectangular form a + bi.

A: Given the complex numberz=10cis315°

Q: Find all the complex roots. Leave your answer in polar form with the argument in degrees.

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Q: Transform the complex number into its rectangular (1+5i)

A: (1+5i)

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

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

Q: Find all complex numbers that are solutions of the given equation. Leave your answers in standard…

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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 all complex numbers z so that z6 = 218 Express your solutions in the form a + bi, evaluating…

A: Given: z6=218 We have z6=236z=23 Let z=rcosθ+isinθ. Then, z to the power 6 gives…

Q: Plot the complex number z = 2 + 5i and find its absolute value.

A: Given:z=2+5i

Q: (a) Find all roots of the quintic equation, in the complex plane and plot them. 25 -1 = 0,

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

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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 &lt; 2π.1 - 3i

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

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

A: Given complex number is: z=2-23i Let us consider, r cos θ=2r sin θ=-23 Then we get,…

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: 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: Z is a complex number

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Q: Express the complex number z = 10 cis 270° in rectangular form a + bi.

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Q: Find all complex fourth roots of -2-2/3i. In other words, find all complex solutions of x=-2-2/3i.

A: follow next step

Q: Find all complex numbers z such that z2=-15+8i, and give your answer in the form a+bi. Use the…

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Q: Find all complex square roots of -2+2/3i. In other words, find all complex solutions of x=- 00..

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Q: Find the cube roots of the complex number. Express in standard form

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Q: Find the 3 cube roots of 1, that is find   11/3 And Plot them in the complex plane

A: The graph can be drawn with real part as x axis  and imaginay part as y axis

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

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

Q: Find the roots of complex numbers. z5 = 4i

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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: Determine the absolute value of the complex number z = 5 + 12i

A: We have to find absolute value of complex number: z=5+12i We know that if we have complex number…

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

A: We know that z=x+iy, then…

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

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

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…

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-2 - 2i

A: Solution: Consider the given complex number is: z = -2 - 2i The trigonometric form of a complex…