2. Complex Numbers: Show that for any two complex numbers, A₁ = a₁ + b₁j and A₂ = a₂ + b₂j, where a₁, a2, b₁ and by are real numbers and j = √-1, we have logo Transform: |A₁A₂| = |A₁||A₂| Z(A₁A₂) = Zλ₁ + Z₂

Q: (b) Show that i³i is real, even though i or 3i is not.

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Q: Find the modulus, argument, principal value of argument, and polar form of the given complex number:…

A: According to guidelines i solve first question only so kindly request you to repost the remaining…

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: (a) zi is the complex number a + jb. z2 is the complex number 6 + j2. Given that the product z, xz₂…

A: The main objective is to find the complex numbers. Also find the roots of the quadratic equation.…

Q: For complex number z and w, prove that zw-wz=z - w if and only if z =w or, zw = 1.

A: We know that , for a complex number|z|2=zz¯and when z is a real numberz=z¯

Q: Find the product in the complex plane 1/4(cos Pi/6 +i sin pi/6) + 8 (cos pi/6 + i sin pi/6)

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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: Each student should evaluate each residue, then comment on other students' answers either by agree…

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Q: i would apprativce it if you could exlpain

A: Given complex numbers are z=2+3iw=5−i So,  (a)  2z+w=2(2+3i)+(5−i)2z+w=(4+6i)+(5−i) Now, combining…

Q: A complex number w is such that ww* - 16√√3i+ 8iw = 0 and Im(w) <5, where w* is the conjugate of w.…

A: ww*-163i+8iw=0Imw&lt;5

Q: If r is real and w complex, what is (w-r)(conjugate of w-r) equal to?

A: Given that  is real and  is complex.We need to find the simplified expression of .We know that for…