(a) Find in the form of re'", the six complex numbers which satisfy the equation z° +32+ 32( v3 )i = 0. Hence show that the values of w satisfying the equation (w-1)“ = [-32(J5)i=32](w+1)° -32(V3)i- 32 (w+1 3 k where a = 3 have real parts given by T and - - - 4 cosa – 5 k = 0, 1, 2, 3, 4, 5.

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A: I am providing the solution of (ii) only as follows below :

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Q: iii) modulus of complex z = e"H equal to а. 3 b.2 С. 1 d. 0

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Q: 1-18 Q2- The complex number z satisfies the equation 4Z - 32 2-1 Then Z =

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A: The solution is as follows below :

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A: w4 + ( 5 + 10 i) w2 - 48 + 14 i = 0   Now consider w2 = z Hence now our equation is    z2 + ( 5 +…

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A: we define the hyperbolic sine function by sinh(z) = ez−e-z 2 and the hyperbolic cosine function by…

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A: z= -4 can be written as z= -4 + 0i  -4+0i is on the negative x axis.

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A: As  many questions are given , I will solve only one : We have : f(z)=z4Let z=x+iy and…

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Q: 3. First, show that if we define the complex number z = a + bi to be the matrix and a a -b -d w = c…

A: given z=a-bba  and w=c-ddc multiply the two complex numbers  zw=a-bbac-ddc=ac-bd-ad-bcad+bcac-bd…

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

A: Solution:-

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Q: 2) The complex conjugate of z is denoted as z. Solve for z in the equation: z – 12 = j(9 – 2z) %3D…

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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

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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

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Q: 1.Determine the solution set to the complex equation z – (8 - j5) z + (40 - j20) = 0. (Hint:…

A: We will find out the required solution.

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