11. Write the quotient of the complex numbers in the standard form z=x+ iy. 3+i 1-2i

Q: Let i denote the square root of-1. For the two complex numbers z = 3e and w = 6e find z. w. Give…

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Q: 12. Use Euler's formula to write each of the following complex numbers in the form a + bi. (a) emi/3…

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Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. * False True

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Q: 8. Consider the complex number z = 5+8i and w = 3– 3i. Write down the real and imaginary parts of…

A: Proceed as shown

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: 5) Compute the fllowing complex numbers in standard arbi form for a, bE R. List all values if there…

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Q: write the standard form of the complex number 7/4(cos(3pi/4)+isin(3pi/4))

A: Here cos3π4=cosπ-π4                =-cosπ4                =-12 sin3π4=sinπ-π4               =sinπ4…

Q: 1-181 Q2- The complex number z satisfies the equation 4Z - 3Z %3D 2-1 Then

A: TO FIND: Z =

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. 1 / z

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Q: Two complex numbers z1 and z2 are given by z1 = 3 + 2i and z2 = − 1 − 4i. Evaluate, (a) |z1z2| (b)…

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Q: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. а. 2 b.…

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Q: (b) Find the conjugate, argument and modulus of the complex number Z =1+i3

A: Recall: If z= x+iy , then (i) Modulus of z , z=x2+y2(ii)Conjugate of z is z¯ =x-iy(iii) Argument =…

Q: 4. a. Present the complex number z in algebraic form z= i°+i(i- 3) b. compute the values of the root…

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Q: Let z be a complex number. Then cos(3z)-i is unbounded in C.* True False

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Q: 2 – i Find the conjugate of the complex number in the form of a + bi. 1– 2i

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Q: If z=3-4i then express these following complex numbers in the form of a+ib: (a) (=+1)(=+i) 2z (b)

A: If z = a + ib and w = c + id then z+w = (a+ib) + (c+id)       = (a+c) + i(b+d)

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: 1-i10 Consider, z=1-i Now, z=12+-12=2 & θ=tan-1yx=tan-1-11=2π-tan-11     ∵The complex number 1-i…

Q: 3. Determine all complex numbers z for which |2z – 1| < 2|2 – i|.

A: The given problem is to find all the complex numbers that satisfies the given complex inequality.

Q: 4. Use DeMoivre's Theorem to find the power of the complex number [4 (cos 50 ° + i sin 50°) ]3

A: Use demovirs theorem

Q: Write the complex number z = 2 - j2 in polar O 2.83245° O 2.832-315° O 2.832-45° O -2.832-45°

A:

Q: 8. Consider the complex number z = 2 + i and w = 7 – 2i. Write down the real and imaginary parts of…

A: Given : The complex numbers z = 2 + i  and w  = 7 - 2i.   To write the real and imaginary parts of…

Q: 1. (a) If z1 = -3 - 5i and z2 = -5 – 7i are the two complex numbers, then %3D 21 + 22 + i123 21 – 22…

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Q: V3 1 (- 2

A: given(-32-12i)20 =(-1)20(32+12i)20 =(cos30+isin30)20 The formula of Demoivre's theorem is cos θ+isin…

Q: Write the complex number z=(1-√3i)2015/(√2cis(7π/6))4028 in an exponential form.

A: cis(x) = cos(x)+isin(x)

Q: What is the algebraic form of the complex number 13 e 12+5i 5-12i 12-5i 5+12i

A: We will use the basic theory of complex numbers to answer this question.

Q: 2. Divide the complex numbers. 7+ 31 7- 3i 20 + 214 20. 21 29 29 1-i 29 – 29i O1+i

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Q: Let z be a complex number. Then Im(-iz+1)= O None of these O sliz-1| O =liz-1| O 2liz-1|

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

Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form

Q: 7. Write down complex numbers in the trigonometric and expone forms a) z = 16i; b) z = –1; c) z =…

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Q: 1. Write the complex number 2 + iv3 in the form of rete

A: We have to solve given problem:

Q: B- The Modulus and Argument of a Complex Number Z is (8, 90°) respectively find Vz4

A: We will find out the required value.

Q: Let z = 3 – Ai, w = 1+ 2i be complex numbers. For both z and w, what is the: • Real part • Imaginary…

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Q: 10. Use i = (0, 1) and y = (y, 0) to verify that -(iy) = (-i)y. Thus show that the addi- tive…

A: i=0 ,1y=y ,0 verify :   -iy = -iy  To find additive inverse of z=x+iy

Q: a

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Q: Let z be a complex number. Then Im(-iz+1)= * O =liz-1| None of these O 2liz-1| <liz-1|

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Q: 17. The argument of the complex number z. where com CO is 1- i 13

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Q: 2. Write the complex number 3 + 5i 5 - 3i in the form a + bi.

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Q: 1. Write the complex number i+= in the form of rele V3

A: The polar form of complex number  is    , where     and  and .

Q: Use Bombelli's approach to find a complex number c = a + bi such that = 18 + 26i where a and b are…

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Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. * True False

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Q: 7. Plot the complex number 3 - 6i

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Q: 2. Write the given complex numbers in the form a + bi. 3 (a) 를 + 을-2유 (b) 2,0 + + 5i 5- 12i (c) 2-4i…

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Q: 2. What is the standard form of the complex number –13.5(cos() + i sin())?

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Q: 3.5. If |2| = 1, then show that az + b 1 bz +a for all complex numbers a and b. ||

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Q: Enter in form a + bi the complex number z which has an absolute value 2 and argument 2/3 π.

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Q: Let z be a complex number. Then cos(tz)+3i is unbounded in C. * False True

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Q: Find all complex numbers z satisfying 23 = 27 i

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Q: Exer. 21–46: Express the complex number in trigonometric form with 0 so<27. 25 2V3 + 2i 4 cis 37 29…

A: Given: The complex number 25) 23+2i. 29) -20i 34) -5.