1- DETERMINE A AND BEC FOR THAT THE FUNCTION: (f:C+a=+b -2 +az +b f(=) = IF = #1-i, 2-1+i (f(1– i) =2 BE CONTINUOUS IN == 1-i.

Q: fl2)= (2+1)" Let z be a Complex number such thot earuations I(frz)) = 0 nd +-1. Howr many possible…

A: It is given that fz=zz+12 Let z=x+iy, therefore it follows:…

Q: #4. Show that equation | 2-1-2|=1 Can be written as 121²2 Re Z-2 Im Z +1=0.

A: Given equation  z-1-i  =1. Show that: z2 -2 Rez -2 Imz +1=0.

Q: Question 2. Let G = R, the set of all real numbers, with the operation @ defined by a+b a@b= for…

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A: This is a problem of complex analysis.

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A:

Q: #7. Find the four roots of the equation Z² +4=0 and use them to factor 24+4 into quadratic factors…

A: Answer:-

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A: According to the problem, we have

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A: Given equation is . Let us denoted it by Now, on compare above equation with We get,

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A:

Q: Let z1 and z2 be complex numbers. Which of the following statements are always true? (i) Re(z1z2)…

A: Complex analysis, modulus of the complex number

Q: 4 Get all the roots of 2(V3i – 1) |

A:

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A: Given: -2+23i

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Q: Express -24-11j 4-5j as a complex number in the form A + Bj. Further, move the red dot in the graph…

A:

Q: #1. Reduce each of these quantities to a real number 5i (1-2) (2-2) (3-2) (a) 1+2i 3-4i + 2-2 5 i…

A:

Q: 2 The roots of the equation X + 2x+ 5 0 a 1) -3 and 1 2) -1, only 3)-1+ 2i and 1- 2i 4) -1+4i and…

A: given equation :

Q: 2 Express (-i)² i 3 3 in 2 simplest a + bi form.

A:

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A: Given: |z+3|+|z-3|=10

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Q: 2. It is easier to find the power or the root of a complex number if the numnber is written in form.

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Q: Plot the complex number. 6/6 - i Imaginary Imaginary axis axis 20 20 10 10 Real Rea – 20_ – 10 axis…

A: To plot and write the trigonometric form of the complex number

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A: Simplify the given complex number as follows.

Q: a

A: