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

Q: Find the modulus of the complex number. -9

A: here we need to find the modulus of given complex number. the solution is following.

Q: Determine the argument and the modulus of the given complex (-2-4i)(5i) number: (3+8i)

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Q: Consider the complex number 2 + i. Working in exponential form, investigate the effect of…

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

A: Given complex number z = -5 + 5√3i.Graph the complex number.

Q: 4. Find the modulus, Iz], and argument, 0 , of the complex number. -1 + i

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

A: Represent the complex number geometrically.(1 + 2i)2

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: Write the complex number in polar form with argument 0 between 0 and 2n. -1 - V3i

A: Given query is to write the expression in Polar form.

Q: N=-7+1li %3D

A: Given complex number Z=-7+11i

Q: Find the modulus and the principal value of the argument of the following powers of complex number:…

A: Explanation of the answer is as follows

Q: Find the modulus of the complex number. -5- i

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

A: given 2i(2+3i) =4i-6=-6+4i It is represented in a complex plane. where x-axis represents real value…

Q: Find the modulus, argument and polar form of the complex number: 1 + i.

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Q: solve the complex number using De Moivre's Theorem 483 ( - V3 2

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: Use DeMoivre's Theorem to raise the complex number to the given power. Express your solution in…

A: Compare the given complex number with the standard form and find x and y.Find theta using x and y.

Q: Find the modulus and argument of the complex number (2+i/3-i)2. Also express -5+ 5i in polar form

A: 2+i3-i2=2+i3-i·3+i3+i2=6+2i+3i+i29-i22=6+5i+-19--12=5+5i102=25+50i+25i2100=25+50i+25-1100=50i100=i2=…

Q: Find the cube root of 4/3 +4i. Graph the roots in the complex plane.

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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: Consider the complex number z = 10250°. What is the smallest positive integer n such that z" is a…

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Q: Find all real numbers a and b such that the complex numbers 21 = a² + 4b – bi and 22 = 4+b- 2 a²i…

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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: If z is a complex number then the sum of z and its conjugate is an imaginary number. O true false

A: Let z be a complex number given by, z=a+ib where a is the real part and b is the complex part of z.

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

A: (1+5i)

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

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

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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: 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: Rewrite the complex number 8e.b in a + bi form. Round to two decimal places.

A: The given complex number 8e1.5 i

Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form

Q: (b) Find the conjugate and modulus of the following complex number Z = /5+ i6

A: Given complex number is z=5-i6 Since, conjugate of a complex number a+ib is a-ib Hence, conjugate of…

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

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Q: Simplify the complex number z = j(-1+ j) and plot the result on your Argand diagram. Then, find the…

A: Given :           z = j(-1 + j)        To simplify z and to plot the result on Argand diagram.…

Q: 2. Write the complex number 3+5i 5-3i in the form a + bi.

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Q: Show that the conjugate of the sum (product, or quotient) of two complex numbers, z1 and z2 , is the…

A: Let z1 = a+ib and z2 = c+id be two complex numbers. Then we get, Conjugate of z1 is = a-ib Conjugate…

Q: What is the cartesian form of the complex number: (-1-i√3)4

A: The given complex number: -1-i34.

Q: a. Find the modulus and argument of the complex number here, x = last digit of your ID number.

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Q: Find the distance between the complex numbers in the complex plane. 71, 4 - 3i

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Q: Represent the complex number geometrically.3 - 5i

A: The complex number 3-5i

Q: Use de Moivre’s formula to find the Cartesian form of the complex number  (-2 + 2√3i)7

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Q: Find the modulus, Izl, and argument, 8, of the complex number. -1+i One charaes 4.6

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Q: 2. Write the complex number 3 + 5i 5 - 3i in the form a + bi.

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Q: The complex number modulus z = 12 - 5i is:

A: Given,         The complex number is z = 12 - 5i .

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: Find and graph all the roots in the complex plane. (3 + i4)

A: this is a problem of complex analysis.

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