1.) Transform the following complex numbers . a. )    i  (into polar form) b.)    6- 3 i   (into trigonometric form) c.)     2 + 2 i      (into exponential form )

Q: 4. -5 Vi + 1/3 5. - V8 - 2i/3 V3 - 10i 6. + 5i

A: Polar form of a complex number z=x+iy is  z=rcosθ+i sinθwherer=x2+y2andθ=tan-1yx

Q: 1- Represent the following complex numbers in polar coordinate Z= 2 + 5j Y= -3 - 3j

A: Z=2+5j compare the complex number with z=a+bj a=2b=5 find the modulus r  r=a2+b2=22+52=4+25=29…

Q: To convert a complex number from rectangular form, z = a + bi, to polar form, z = r(cos e + i sin…

A: We fill the blank spaces as,

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

A:

Q: Convert the complex number, z = 5cis(330°), from polar to rectangular form. %3D Enter your answer as…

A:

Q: Convert the complex number from polar form to rectangular form, a+bi. 5n 14.7 cos 5n +i sin 6 The…

A: The polar form of the complex number is given as 14.7cos 5π6+i sin 5π6 The polar form of the complex…

Q: Plot the point corresponding to, z =2(cos30ο +isin30ο ) in the complex plane, and write an…

A: z = 2(cos 30° + i sin 30°)

Q: 1. Write the polar form of the following complex number Z = 3

A: We know that polar form of complex number z=x+iy is z=r(cosθ+isinθ) Where r=x2+y2θ=tan-1(yx)

Q: Consider the complex numbers: z = 2 – i and w = 1+3i . Sketch (in the same diagram) 2, w, zw and z:

A:

Q: Find the rectangular form of the complex number z that is given in polar form: z = 2.7(cos 1.9 +i…

A: Put x=r cosθ   and   y= r sinθ

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

A:

Q: Find the product of the complex numbers: z, = -V3+3i and z2 =1+ 2i in polar form.

A: Given:          z1=-3+3i          z2=1+2i         product of complex number =z1×z2…

Q: Convert the complex number from polar form to rectangular form, a+bi. 15.1 cos+i sin :) The…

A: Given,  The complex number  15.1cosπ4+isinπ4  We have to write it in rectangular form a+ib

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

A:

Q: 11.Write the complex number 3e in polar and rectangular form

A: Given:     Z = 3ei(4π/3)

Q: Find the quotient z1/z2 of the complex numbers z1 = 2 + 2i and z2 = 1 + i. Leave answers in polar…

A: Given: z1=2+2i , z2=1+i To determine: z1z2. Also, to write answer in polar form.

Q: 1- Represent the following complex numbers in polar coordinate Z= 2 + 5j Y= -3 3j D= -2 + 6j 2- Find…

A:

Q: When a complex number z is written in the polar formz = r(cos θ + i sin θ), the nonnegative number r…

A: Given- When a complex number z is written in the polar form z=rcosθ+isinθ, the nonnegative number r…

Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: -1 - sqrt(3)/3 i = -1 - 0.577i (approx) This is similar as (-1,-0.577). Plotted it on graph.

Q: 15. Express the given complex number in standard polar form. 5 п -2cis 4 O a. √√2+√2i O b. √2+8i OC.…

A: Given;  -2 cis(5 pi/4) Repost the next question.

Q: Express the complex number z = 9√3+9i in standard polar form.

A: The given complex number,    z=93+9i

Q: I. Write 2 – 7i in polar coordinates on the complex plane.

A:

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

A: A complex number 2+5i-4-7i is given. First simplify the complex number by rationalizing it. For…

Q: If the complex number z = x + iy satisfies the condition |3z – 6i| = 3, then z lies on %3D a. Circle…

A:

Q: IV-1 Find the roots of the following complex numbers in polar form, correct to 3 decimal places. [4…

A: Thanks for the question :)And your upvote will be really appreciable ;) Correct Option :- C

Q: 7. Rewrite the complex number 4 + 7i into polar re" form.

A:

Q: Which of the following complex numbers is written in Polar form? a) z = 1 - j b) z = 1Z5 c) z =…

A: The polar form of a complex number is- z = r(cos θ+i sin θ)=reiθ

Q: 12. Write the complex number -4 + 4i in polar and exponer

A:

Q: What is the product (4/3 – 4i)( /2 + V2i) in polar form? In what quadrant of the complex plane does…

A: First multiply both the factors and then find magnitude and the angle to convert it in the polar…

Q: 5+ V4 i = Z 5-6i

A:

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: Convert the given complex number form z = 4+7i into polar form

A:

Q: Convert the complex number from polar to rectangular form. z = 9 (cos(7pi/6)+i sin(7pi/6))

A:

Q: Represent in polar form and graph in the complex plane as 1.1+i 2. -4 + 4i

A: Polar form of the complex number

Q: 6 Convert your original pair of complex numbers to polar form. D = 1-j2

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (3+ /3i) (-1-i)?

A:

Q: Convert the complex number 9/3 9 i to polar form. Give exact answers for r and 0 (no decimals).

A:

Q: (a) Make use of De Moivre's Theorem to calculate (3√3+3i)5 and leave your answer in the form a + ib.…

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

Q: b) Convert the following complex numbers (rectangular form) to polar form i) z=5+ jl0 ii) z= 10- j21…

A:

Q: Express the complex number z = 6 cis 0° in rectangular form a + bi. Provide your answer below:

A:

Q: Write the complex number in polar form with argument 0 between 0 and 2m. -VZ+ V6i

A:

Q: - find polar form of the complex number z = (2√3-4i) + (-√3+51)..

A:

Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

A:

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…

A:

Q: What is the polar form of the complex number z = 3i? Z.

A: Given that z = 3i and find that what is the polar form of this . Here i attached solution of this…

Q: Express the given complex number in rectangular form into polar form. -5 – 5i3 ○ 5/2 [cos(플) +…

A:

Q: Convert the complex number 9/3 9 i to polar form. Give exact 2 2 answers for r and 0 (no decimals).

A: The polar form of the complex number is rcosθ + isinθ. The formula for finding r is a2+b2 and the…

Q: Convert the complex number 8 cos +i sin to polar form. Give exact answers for r and 0 (no decimals).

A: