1) If we have the following complex numbers: Z, =2+3i, Z, =3-2i %3D Z, (d) Find (a) Z, + Z2 (b) Z, -Z2 (e) Z,Z2

Q: Determine the argument and the modulus of the given complex (-2-4i)(5i) number: (3+8i)

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Q: (a) 2122 + 22Z3 + 2321 (b) (c) Re(z) +Im(2?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Express the sum of (2 - 3i) and (6 + 4i) divided by the sum of (4 + i) and (-5- 2i) in a + bi…

A: 1)  To find the value of           {(2-3i)+(6+4i)} / {(4+i)+(-5-2i)}

Q: 3. i 5. (5 -91) + (2- 4i) 7. i(5+ 7i) 9. (2 - 3i)(4 + i) 4 i" 6. 3(4 - i) - 3(5 + 21) 8. i(4 – i) +…

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Q: Calculate: 4+ 3i (a) -1- 3i (b) (1 + i)(3 – 4i)(4 – i) = i(2 + 2i)³ | (c) (3 – 2i)² ||

A: Given that: (a)4+3i-1-3i(b)(1+i)(3-4i)(4-i)(c)i(2+2i)3(3-2i)2   NOTE: As per our answering…

Q: Find the conjugate of – 3i ( 2 + 5i ).

A: Solution

Q: Solve, z2 - 4z + 5 = 0 Given that z, = 3 + i, z2 = 4 – 3i, z3 = -1+ 2i and z4 = -2 – 5i, determine…

A: Given equation is, z2-4z+5=0 Now, z=4±16-4×52⇒z=4±-42⇒z=4±2i2=2±i So, the solutions are z=2+i, 2-i

Q: Let A = [3 – 2i 4i 1+ 6i], and B = [5+i 2 – 3i 5]. Find (1 - 2i) A + (3 + i) B. %3D

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: If z = 1+ 2i and w = 3+ 4i, express the following in the rectangular form: (a) 2|w| +(1 – i)2² w + z…

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Q: 1. Which of the following is a complex solution to the equation: (x+3)* -4 =-40? (1) 3+7i (3) -3 +6i…

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Q: Which of the following is a complex solution to the equation: (x-2) +8=-17? 1) 2-5i (3) -2+3i 2) -2…

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Q: (A) Given A = 3i + 5j , B = -4i + j Find the à +B , à – B & Ā. B

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Q: 5. Simplify to a C. Write answers in the form a + bi a, beR (g) (1+3i)(1 – 4i) (h) (5 – 2i)(-1+ i)…

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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: Find x and y given that (x+yi)/2+i = (1-i)/2+3i

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Q: 2. Write each of the functions in the form Aet cos Bt +iBed sin Bt, where a, B, A, and B are real…

A: To write each of the given function in the form  A* eatcos(bt)+Beat sin(bt) . We apply three…

Q: 4+ 3i 3 — 5і (b) 2+ 3i 2 – 3i

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Q: Simplify completely: 22+5 3z +. z十1 z-2

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Q: 2+j = j(x+ jy) 1- j

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Q: (a) Simplify the following () 62 (i) V-180 (b) For the complex numbers 21 = 8+ 15j and z2 =-3 + 8j,…

A: →j2 = -1→j4 =j2 × j2 = -1×-1 =1             So, j4k =1 , where k is any natural number.→Let z= x +…

Q: If A = -4 + 2i and B = 3 – 5i, in which quadrant does A + 2B lie?

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Q: Express e a) 0-e²i b) 0+e²i c) e² - ei c) e² +e²i in a +ib form.

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Q: Solve the complex number z = (2+3i)^3/2

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Q: If Z=x+iy and 3x+(3x-y)i=4-6i then Z . * -4/3+10i O 4/3-10i O 4/3+10i -4/3-10i

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Q: Write each of the complex numbers in the form a + iß, where a and B are real numbers. (a) 2ei/3 (b)…

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Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

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Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i

A: To simplify the given complex expression:- 5-i3-i

Q: 2こx+iy 2 Recz) =l 3-i1 if 121 =2, then

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Q: Verify that (¹)² = i²i but that (i²)i ‡ į²i ("i" imaginary unit)

A: What is Complex Number: A real number and an imaginary number are effectively combined to create a…

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: If z₁ = 5-i, z₂ = 1-2¡ then evaluate 32₂ +22₁-5- z, 2z, -3z₂ +3-i

A: Use complex number concept

Q: Find the value of x in the complex equation (2x - 3yi)(3 + 4i) = 78 - 21i %3D

A: Given complex equation (2x-3yi)(3+4i)=78-21i To determine the value of x  First multiple left hand…

Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: Given: Complex numbers are z1=2+j3, z2=-1-j2 and z3=4+j4. To find:…

Q: Calculate the following. - 2+4 i (C) (-2+5 i) - 1- 5 i - 3+3 i 4+2 i 5+3 i (a) 2+ 4 i (b) - 5i - 3+3…

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Q: What is the image of the line x = c; c > 0 in the function f(z) = ? ("z" complex number) Z

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