Let A= 3010 0401 000 0 100 - a) find det (A) b) find the inverse c) solve the system Ax= of (A) ONT

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: 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: 8 12 F dt 2.

A: Given: I=∫148t-12t3dt   As we know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule:…

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

A: Solution

Q: Suppose the complex numbers x and y satisfy the following equations: xy - y² xy + 2x² = = 3 1 (A) 8…

A: Answer is D. 16

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: 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: Use the adjoint method to compute the inverse of

A: If A is any matrix, then inverse of A is, A-1=1AadjA Where…

Q: Q4) Answer two only 5-3i, a) Evaluate i 2+4i b) solve the following to find c and d (3-2 i)(c+id) =…

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Q: solve Væ – 5+ Va + 2 = VII 11 -103/11 O -59/11 59/11

A: Solution :-

Q: Solve for the matrix X eMz (R): -2 3 ļ s X = 7|o

A:

Q: Find the value of q such that (3 + 4i)(1 + 2i) (1 + 3i) = q(1 + i).

A: We have to simplify left hand side expression then compare both side to find the value of q.

Q: Solve the first order PDE -2и, + 6и, — 0, и (4у, у) — 2у + 1

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Q: Solve the following using the inverse matrix method: 2x - y + 3z = 9 x+y+z = 6 x-y+z=2

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

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Q: number (1 – 2i) c.+ 2 C. =+=i d. 1+

A: 1. logi(2i)=logi(2)+logii=logi2+1This is the required simplest form.

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

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Q: Compute: 19 (4-2i)(4+2i)

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Q: Find the matrix exponential of -3x1 + 8x2 x2 = 12x1 – 7x2 and use the matrix exponential to solve…

A: Given that  x1'=-3x1+8x2x2'=12x1-7x2 and the initial conditions are x10=1,x20=-1 The objective is to…

Q: Write i -1 - i in x + iy form.

A: Here we use that i=exp (πi/2).

Q: Find all critical points of the given plane autonomous system. (Order your answers from x' = -x(4-…

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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: Q.2) Use Inverse matrix method to solve the following equations: *- y +z = 1 2r – 2y + 2: = 2 -3r +…

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Q: m(x)= 14x-1 3 서 2

A: Given : m(x)=4x-132 To find : Find the inverse and prove it by composition.

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

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Q: A =  3i - j + 2k B = 2i + j - k  C = i - 2j + 2k solve for a.) (A x B) x C b.) A x (B x C)

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Q: Find the value of a such that (3 + 4i)(1+2i) (1 + 3i) 9 = = = q(1 + i).

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

A: Use complex number concept

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: (a) If j² = -1, simplify

A: (a) if j2=-1, then      (i) j6=

Q: Find the value of S in (3A +4Si)(6-7i) = 3+5i

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Q: m(z + 3i) = 6

A:

Q: Diagonalized  if possible, where is A=[■(4&0&1@1&1&0@3&0&1)].

A: Given A =   4 0 1     1 1 0     3 0 1