7. Write down complex numbers in the trigonometric and exponential forms a) z = -21; b) z= 5; c) z= 2- 2V31.

Q: Consider the complex number 2 + i. Working in exponential form, investigate the effect of…

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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: What happens when a complex number is multiplied by its conjugate? It turns into a real number…

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Q: Find the quotient z1/z2 of the complex numbers z1 = cos 80° + i sin 80° andz2 = cos 200° + i sin…

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

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Q: A number of the form iy is called pure imaginary ylgn İhi

A: True

Q: 2) Suppose 1 and w are complex numbers, show that Aw =

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Q: iv) in complex number z3. (7)? = |z|?. z

A: Complex number: A complex number has the form z=x+ιy, where x is called the real part and y is the…

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

A:

Q: Write down the complex number 1 + V3i in polar form. (Hint: notice that cos (중) -글)

A: The polar form of a complex number a+bi is r(cosθ+isinθ) where r is the absolute length of the…

Q: Let z be a complex number. Then coth(2+7ti) is equal to cothz -cothz tanhz None of these -tanhz

A: Solution

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

A:

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?

A:

Q: 3. If z, and zz are two complex numbers, prove that

A: Let's find.

Q: How many complex numbers z with |2| = katisfies the equation 2 %3D

A: z=1⇒z2=1⇒zz¯=1⇒z¯=1z

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

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Q: If 2 complex numbers z, and z, have the same modulus then they must be equal. Select one: O True O…

A: Let two complex numbers 2+i and  z1=2+i=22+12=5z2=2-i=22-12=5

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: 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

A:

Q: What is the result of multiplication of complex numbers -V3+i and 끓 (cos +isin )? A 을 (cos +i sin )…

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Q: Given the complex numbers  z = 8 (cos(8π/15) + i sin(8π/15))  w = 1/2 (cos(17π/15) + i…

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

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Q: 13 Jlgull If z,,z, are two complex numbers then:

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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: 11. The vertices of an equilateral triangle are equidistant from the origin. One of its vertices is…

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

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Q: . Ifa complex number z has modulus 2 and argument , then

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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: Find all the solutions of   18 sinz = 1.  note: z is a complex number, so please solve for the…

A: Please check step 2 for the solution.!

Q: 2. It is easier to find the power or the root of a complex number if the numnber is written in form.

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Q: Express the result in trigonometry and rectangular form (1 + 2i)4 44. (1 – 2i)?

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Q: The variable z is often used to denote a complex number and 7 is used to denote its conjugate. If z…

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

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

A: Suppose complex number Z1=a1+ib1=2+3i and Z2=a2+ib2=-1-2i (a) given complex number 3Z1-2Z2…

Q: Let z be a complex number. Then i(cosh(3z)+sinh(3z))=e^(3z)?

A: Explanation of the answer is as follows

Q: 4. Use DeMoivre's Theorem to find the indicated power. Write answer in rectangular form.

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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: Let z be a complex number .then e^(3z+i) is bounded over the set of complex numbers?

A: Let z is a complex number. Let f(z) = e(3z+i)  Let us assume that f(z) is bounded. Hence f(z) is an…

Q: Show that if z1 and z2 are complex numbers then (z1/22) = Zī/22.

A: Given, z1 and z2 are two complex numbers and we have to show,

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

A: according to bartleby guideline, I can solve first question...

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

A:

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: Use DeMoivre's Theorem to find the indicated power of the complex number [2(cos 48°+isin 48°) State…

A: r(cosθ+i sinθ)n=rn(cos (nθ)+ i sin (nθ)

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

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

Q: If a is a complex number such th equation az²+z+1=0 has one p

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.