Vz + i/3 V3 - 10i 5. 6. -V8 – 21/3 -V3 + 5i

Q: 4. -5 Vi + 1/3 5. - V8 - 2i/3 V3 - 10i 6. + 5i

A: Polar form of a complex number z=x+iy is  z=rcosθ+i sinθwherer=x2+y2andθ=tan-1yx

Q: 2- j in polar form. Express the principal root in 1+ j2 07 Find the three cube roots of

A: Let z= 2-j1+j2=2-j1+j2×1-j21-j2=2-j4-j-21+4=-j55z=-j x+jy=-j

Q: Q2\ If z = 1 + i, what is z3 + z? + z + 1 as a single complex number?

A: Use the following formulae, to simplify the given expression.…

Q: -4/2 – 4V2i Express the complex number z = in polar formr cis 0.

A:

Q: Plot the point corresponding to, z =2(cos30ο +isin30ο ) in the complex plane, and write an…

A: z = 2(cos 30° + i sin 30°)

Q: Q4) a) Find the polar form and represent graphically the complex number 7-5j b) Express…

A: We have to find Polar Form of Complex Number 7-5j We have to express 3cos232°+jsin232° in…

Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: To find the fourth roots of -1 the De Moivre's formula convert the rectangular co-ordinate to polar…

Q: Represent in polar form and graph in the complex plane as 1. 1 + i 2. -4 + 4i 3. 2i, -2i 4. -5 V2 +…

A: For any complex number z=x+iy the polar form is r,θ where, r=x2+y2 and θ=tan-1yx.

Q: Find all solutions of z E C of the equation i(z + 2i)4 = -81 and hence show via the sketch all these…

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Q: Find the complex conjugate z¡ of z1 = –7i + 6. Z1 = %3D

A: conjugate of a function means change the sign of i term

Q: 2) The complex conjugate of z is denoted as z. Solve for z in the equation: z - 12 = j(9 – 2z)…

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Q: Find the complex conjugate z of z1 = -2+ 8i. %3D %3D

A: We have to find the complex conjugate {\displaystyle {\overline {z}}}1 of  z1 = -2 + 8i

Q: (b) If z = x + iy is a complex number. Sketch the curves in the complex plane given by i. Im(2) = –1…

A: i. Given that Imz=-1. This implies that, Imz=-1Imx+iy=-1y=-1 Sketch the curve Imz=-1 as shown below.

Q: 29. When z = z If z and z are equal, what can you say about the location of the point z in the…

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Q: Im(z – i) = Re(z+4 – 3i)

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Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = I(z − 3i)|…

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Q: The complex conjugate of z is denoted as z̄. Solve z in equation: z-12=j(9-2z̄) giving the answer…

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Q: 3. Find the polar form of the Cartesian equation: x² + y² = (3 + 2x)² %3D

A: Solution-

Q: 2. Find the set of points satisfying the equation in the complex variable z: |2* + 2i| = |3(z – 3i)|…

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Q: (15) For the complex number z = ti find z2 by a) directly multiplying in the rectangular form given,…

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Q: 1. Describe and sketch the curve in the complex plane given by 2|z| = |z-2| Also write your final…

A: We have to Describe and sketch the curve in the complex plane given by2|z| = |z-2|Also write your…

Q: 1.4 Describe and sketch the curve in the complex plane given by 21리 3 1z- 21. Also write your final…

A: We have to Describe and Sketch the curves in the complex plane given by 2|z|=|z-2| Also write final…

Q: b) Given the complex number z = -V32 + V32i. i. Express z in polar form. Vz and sketch ii. Obtain…

A: ----------------------------------------------------- Given: z = -32 + 32iAim: To express 'z' in…

Q: 1.4 Describe and sketch the curve in the complex plane given by 2|2| = |2 – 2|. Also write your…

A: We assume z=x+iy then we put this value on the given equation to find the curve and from curve we…

Q: Find the first cube root of the complex number z = 512 Cis(180°) of the form a + bi Ob.4v3-4i Od.4 +…

A: Given z=512Cis(180°) Formula: nth roots of complex number z=a+ib are given by zk=r1ncosθ+360°kn+i…

Q: Find the distance between the points 2+3i and 5 -2i in the complex plane. (Round your answer two…

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Q: 5) A = 2i+3j+5k and B = 3i+6k, Determine the direct cosine of (AXB). %3D %3D

A: Finding the cross product of vector A and vector B  i×i=j×j=k×k=0, i×j=k, j×k=i, k×i=j, j×i=-k,…

Q: Find the four fourth complex roots of z = – 256. Express your answer in polar form and then convert…

A: So,

Q: (b) Shade the region in the complex plane defined by z+1+i 2-1-5i

A: Solution:-

Q: Q3. Given the complex numbers z1 = -V3 +i,z2 = 2 - i,z3 = -V3 – 3i and z4 = 4 + 4i 3.1 Represent the…

A: We have to solve given Questions

Q: Find the location of z = -3-4i on the complex plane and find |z|.

A: The given complex number is z=-3-4i Compare with,

Q: Plot the points z = 3+9i and w = 7+5i on a complex plane ană find distance between

A: Plot the points z = 3+9i and w = 7+5i

Q: ) Find the Cartesian form (i.e. æ + jy where x, y E R) for the complex number 1 (2+ j)(1 – 2j)´ - )…

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Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = |F(z – 3i)|…

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Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2- j3 5z 1+…

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Q: Represent in polar form and graph in the complex plane as 1. 1 + i 2. -4 + 4i 3. 2i, -2i 4. -5 V2 +…

A: The given problem is to evaluate and simplify the given complex expression and represent in the…

Q: 4. Find the product of z1 = -8+3i and z2 = 6-9i in polar form %3D

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Q: 2n Express the complex number z = 8 cis 4 in 3 rectangular form a + bi. Select the correct answer…

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Q: 10 + j5 +3440° - 3+ j4 Evaluate this complex number: +10230° and represent it in the polar form,…

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Q: 5. Determine all roots of the equation z4 – 9 = 0, and sketch them on the complex plane.

A: Given equation:                            z4-9=0

Q: Find the quotient of z1 = -6+2i and z2 = 7+8i in polar form %3D %3D

A:

Q: Find all points on the complex plane which represent the complex numbers w = (V3- 1)z+1-2i, given by…

A: We know that, z=2eiϕ, ∀ϕ∈ℝ implies the circle of radius 2 with center at origin. Graphically: Now,…

Q: d graph in complex plane the fo V3 – 10i 1 V3+5i

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Q: If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on Circle with…

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Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: Given the complex number 18 in polar form and rectangular form.

Q: If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on Select one: х…

A: Given that: z=x+iyCurve: |z+1|=1

Q: Express the complex number z = 8 cis 300° in rectangular form a + bi. Select the correct answer…

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Q: It is given that z = x+ iy where x and y are real numbers. Find the complex number z such that z+3z…

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