1. We want to prove that division for complex numbers is just a multiplication of inverses. Recalls that the multiplicative inverse of a number w is 1/w. Specifically, we want to show that for any two complex number z and w, z/w = z . 1/w. Prove this by performing the divison for the left-hand side, then find the inverse for w and then perfom the multiplication on the right-hand side.

Q: Simplify the complex number i .45 as much as possible.

A: See solution below

Q: 7. Multiply the following two complex numbers: (4 - 5i)(-2 + 7i)

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Q: Transçorm the complex number into its tectangulan and exponential form.

A: We use transformation formula to write it in exponential form. The given complex number is already…

Q: 13. Use the exponential form of a complex number to write a + ib. ++) in the form

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Q: Let zand w be complex numbers with the following properties. |z| = 7, |w|= 3, Arg(z) = − and Arg(w)…

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Q: Write the following complex numbers in exponential form. The principal value of ал the argument…

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Q: 111. Give an example of a complex number that is its own conjugate.

A: Given, Give an example of a complex number that is its own conjugate.

Q: What is the multiplicative inverse of the complex mumber z = 2-5i? 2 В. 29 29 c (1) D. (;=) А. C.…

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Q: Multiply the complex numbers 15+j4 and 12+j4

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Q: Suppose the product z1z2 of two complex numbers is a nonzero real constant. Sho 2 kz1, where k is a…

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Q: Take the last four digits ABCD of your student identification number, and let z1= A + Bi and z2 = C…

A: Here, z1=5i z2=6+4i

Q: find quotient 1/z for given complex number z=-sqrt 3 + i

A: The given complex number is z=-3+i. The conjugate of the given complex number is as follows. z=-3-i

Q: b. Z1= 4(cos 200° + i sin 200°), z2= 25(cos 150° + i sin 150°)

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Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) -…

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Q: 1. Simplify the following list of complex expressions to the form a + ib where a, b are real…

A: we need to simplify the given complex expression to the form a+ib we know i=-1,  i2 = -1,  i3=-i, i4…

Q: Simplify the complex power [(1+i)/(1-i)]-2i  and leave your answer in its simplest form.

A: Use the following formulae, to obtain the solution.…

Q: Simplify the complex rational expression by dividing.

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Q: Apply your results from the previous two activities to findadditive and multiplicative inverses for…

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Q: a

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Q: 2. Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: 8 1. Convert complex nos. into standard form (→ √3 – i)ª

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Q: a)(a +5b)(2a-3b) b)3x (x-3y)-(x-3y)•(-3x+y)

A: