Which of the following complex numbers is equivalent to 3 - 5i ? (Note: i = -1) 8 + 2i 5i 3 A) 8 2 5i 3 B) 8. 23i 7 C) 34 34 23i + 34 7 D) 34

Q: Given the complex numbers a and b such that |a|=|b|=|a-b|=1. The numbers a and b verifiy the…

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Q: Suppose Zi and Z, are two given complex numbers. Construct graphically a. 3Z1 – 2Z2 b. (1/2)Z, +…

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Q: In the complex number 3 + 4i, the absolute value is: А. 3 В. 4 С.5 D. 6

A: Solution

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: Express the following complex number in its polar form. 2+5i 6.- -4-7i

A: Solution :-

Q: In an Argand diagram, O is the origin and the points P and Q represent the complex numbers z1 and z2…

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Q: 13 8 cos 37 + i sin 8 |10 + i sin 16 Cos 16

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Q: 2. If a and b are complex numbers, and z is a complex number that obeys |z| = 1, show that az + b =…

A: Given that a,b and z all are complex numbers.   let, a=c+idb=r+is  and z=x+iy, where c,d,r,s,x,y all…

Q: The 8th roots of a complex number would have arguments that differ from each other by ??? degrees.

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

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Q: Let z be a complex number. Then cot(5z-pi) = cot(5z)?

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

A: Given that, 2+23i10

Q: Given the complex number o=• V3-i, (a) find the modulus and argument of o (b) in the form a+bi .…

A: Here we find the modulus and argument.

Q: Pick two complex numbers (like a + bi and c + di) and consider if the following statement is True or…

A: Set of pure imaginary numbers

Q: Given the complex numbers z = 24( cos +i sin and w = 4( cos +i sin 3 3 find giving your answer in…

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Q: Given two complex numbers z = 3 – 3j and w = 1 + 7j which of the following options equals

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Q: Given two complex numbers z 3-3j, and w =1+7j, %3D which of the following options equals ?

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Q: Given a complex number a + bi, the value of a is called the _____ part and the value of b is called…

A: The given number is a+bi To identify a and b

Q: p and q are complex numbers such that pl = 7√3 and lp + ql = 12√2. - On what interval must q fall…

A: Use  Cauchy inequalities and solve the question.

Q: The complex number (−9+7i)/(9+5i) rewritten in Cartesian form is?

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Q: Use the help of the polar representations of complex numbers to express (V2 + i)? in the form of a +…

A: Given, i=-1 2+i2

Q: To convert a complex number z = x + yi from standard form into trigono metricform, use the…

A: The modulus of a complex number z=x+yi is r=x2+y2 & the amplitude or argument is,…

Q: If 'a'is a complex number such that z = 1. Find the value of a, so that the equation az? +z+1=0 has…

A: Explanation of the answer is as follows

Q: Evaluate b. Topic under Cartesian Complex Numbers

A: Given, -1j7

Q: Let z be a complex number. Then coth(2+ Ti) is equal to None of these tanhz -tanhz oothz

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Q: If =1-i and =5-21 then draw the following complex numbers on the Argand Diagram: (a) 2, + (b) 4-4…

A: The objective of the question is drawing the given complex numbers on the Argand plane (diagram).

Q: 2. Identify the conjugate of each complex number, then plot both complex numbers and their…

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Q: Which of the following complex number is represented in the Argand diagram shown? -1 -1 1 2 --1- --2…

A: If we have a complex number a+ib Here a is the real part of the complex number and b is the…

Q: Find a complex number for which Arg(z bar) does not equal -Arg(z).

A: For all non zero complex number we have Arg(z bar) = - Arg (z)  as if z = x+iy  which imples z¯ = x…

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: r(cos x + i sin x)= r eix

Q: Evaluate the complex number: (cos 20+i sin 20)² (cos 30 + i sin 30)2 (cos 40 + i sin 40) (cos 60 +i…

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Q: Let z be a complex number. Then cot(5z – n) is equal to

A: Since solve the first question for you. If you want any specific question to be solved then please…

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: By plotting the points on a scratch piece of graph paper, determine which complex number has the…

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Q: Let z be a complex number. Then coth(2+ Ti) is equal to -cothz tanhz O -tanhz O None of these

A: I have solved bothe examples for first question first option is correct And for second question last…

Q: Let z, and z, be the complex numbers given in the following argand diagram. Find the complex number…

A: First I am going to find the complex number by using the Euler's identity and then solve the problem…

Q: Given the complex numbers zi = 20 cis 226° and 72 = 5 cis 76°, find the quotient . Z1 Z2

A: z1=20cis2260=20cos2260+isin226°=20ei226°z2=4cis76°=4(cos76°+isin76°)=4ei76°

Q: In Exercises I through 8 use the parallelogram law to form the sum and difference of the given…

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Q: Simply the each of the following complex numbers (4i – 3)(3 + 4i) a. -

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Q: The polar form of complex number (z=3+3i) is O 3 (cos 45+ i sin 45) √2 (cos 45 + i sin 45) O 31/2…

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Q: Convert the complex number, 6las aism Cos पु. + tSh i sin II into atbi form, Show Work, your

A: Given Complex number:

Q: Find the argument of the complex number 3 + 17i 4 4. 47

A: Given complex number is- 3+17i We need to find argument of the given complex number. For any complex…

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

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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: The argument of the complex * number (1+i)^4 is

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Q: Let z be a complex number. Then cot(5z-pi)=coth(5z)?

A: According to the given information, it is required to check whether the given statement is true or…

Q: Let z be a complex numbers. Then cot(5z-pi)=?

A: The objective is to find cot(5z-pi).

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

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