The complex number a is given by a =-2 + 5i. i) Write down the complex conjugate a*. a +a* ii) Find in the form a + bi.

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

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

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Q: Write the complex number in polar form with argument 0 between 0 ánd 27. 7/3- 7i

A: Given complex number z=73-i 7 We can represent complex number z=x+iy into polar co-ordinates rcos…

Q: use the parallelogram law to form the sum and difference of the given complex numbers and then…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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Q: Write the product of complex numbers in the form a + bi. (3 + 3i)(2 + 4i) =    (6 − 2i)2 =…

A: I²=-1

Q: In an Argand diagram, O is the origin and the points P and Q represent the complex numbers z1 and z2…

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

A: Recall: If z= x+iy , then (i) Modulus of z , z=x2+y2(ii)Conjugate of z is z¯ =x-iy(iii) Argument =…

Q: Find the distance between the complex numbers in the complex plane. 1 + 4i, -1 + 7i

A: The distance between the two complex numbers, z1=a+bi and z2=c+di in the complex plane is  In the…

Q: (b) Given z is the conjugate of a complex number z such that z=6+8i Find the complex number z whose…

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Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: -1 - sqrt(3)/3 i = -1 - 0.577i (approx) This is similar as (-1,-0.577). Plotted it on graph.

Q: Find the complex number z that satisfies 3z + 5z = |2|2 + 8i.

A: The given problem is to find the complex number which satisfies the given complex function, We have…

Q: Given the complex number o=• V3-i, (a) find the modulus and argument of o (b) in the form a+bi .…

A: Here we find the modulus and argument.

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

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Q: In the complex plane, the complex number a is identified by the vector OA. Find the midpoint of the…

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Q: Find the product of the complex numbers z1 = 1 + i and z2 = -1 + i. Leave answers in polar form.

A: z1=1+i  &  z2=-1+i

Q: Given two complex numbers z 3-3j, and w =1+7j, %3D which of the following options equals ?

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Q: b) Express the complex number in polar form -4 + 4i

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Q: The complex number (−9+7i)/(9+5i) rewritten in Cartesian form is?

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Q: (b) Give an example of a complex number z, other than ±1 or ±i, such that |2| = 1.

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Q: the complex number z =(2)sqrt2.(e3pi/4) is in eulers form. writing z in the form a+ib. what are the…

A: Given : z = 2√2 ei3π/4

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

A: The given complex number is, 1+i12. The objective is to change the given complex number to the form…

Q: If z and z are conjugate complex numbers, find two complex numbers, z = : = z; and z = z,, that…

A: Note some result about complex number : Suppose z is a complex number then there exist a,b∈ℝ such…

Q: what is the product of the complex number 3-4 and 8e53.13i

A: First convert 3-4i to magnitude and angle form then multiply to 2nd one. We get finally 40.

Q: Find the distance between the complex numbers in the complex plane. -5 + i, -4 + 5i

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Q: What is the complex conjugate of a complex number a  bi?

A: The given complex number is a+bi. Here a and  b  are real numbers. The real part is a and the…

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

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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 complex number 1, where z, = 3-2.j, z, = 1+4j. Za

A: We need to find the Complex number z1/z2 where z1=3-2j and z2=1+4j.

Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: Graph the given complex numbers as shown below.

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: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: Given, z1=2+2iz2=1+i

Q: Find the product of the complex numbers z1 = 1 + i and z2 = 2 + 2i. Leave answers in polar form.

A: First multiply the given complex numbers. z1·z2=1+i2+2i=2+2i+2i-2=4i Obtain r. r=42r=4

Q: Find the sum and the product of the given complex numbers. Plot a quadrilateral with the origin, the…

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Q: Show the 2 points that satisfy the equation in the complex pione. i) | 2 - 11 = 2.12 +1|

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Q: Consider the complex numbers 6v6 11 + V2 3 11 and + 5 W = - = 2 v2 Write in the form reto |wz|

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

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

Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Find the distance between the complex numbers in the complex plane. -2 6i, 6 + 5i

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Q: Find the values of a, b,and c for y = x-6x +5. , b = ,c= Find the complex number. real imaginary…

A: Topic :- Algebra and complex number

Q: Find the argument of the complex number 3 + 17i 4 4. 47

A: Given complex number is- 3+17i We need to find argument of the given complex number. For any complex…

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: Find all complex number solutions to the equation x^y =y^x , where x and y are both nonzero.

A: We need to find all complex number solutions to the equation xy=yx, where x and y are both nonzero.…

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

A: We know that z=x+iy, then…