Write each complex number in rectangular form. (a) 31cos 30° + i sin 30°2 (b) 4 cis 40° (c) 31cos 90° + i sin 90°2

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-2 - 7i

A: z=-2-7i Now, r=-22+-72=53 & θ=tan-1yx=tan-1-7-2=π+tan-172      ∵The given complex number lies in…

Q: Write the complex number in rectangular form.   5 cis 60 degrees

A:

Q: Represent the complex number geometrically.(1 + 2i)2

A: Represent the complex number geometrically.(1 + 2i)2

Q: I. Write each complex number in polar form. 1. 4√3 + 4i

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 + 2i

A: z=-4+2i Now, r=-42+22=20=25 & θ=tan-1yx=tan-12-4=π-tan-112     ∵Given complex number lies in…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.√3 + i

A: 3+i

Q: Express the complex number in exact simplified rectangular form.

A:

Q: Write the complex number in polar form with argument 0 between 0 and 2r. 5 + 5/3i () 101 cos + i sin…

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-10 + 10i

A: We have given  z = -10 + 10i    Now, z can written as reiθ    r =  (-10)2+ 102              [ As if…

Q: Convert the complex number to rectangular form. 8( cos 1 +i sin 1-π) 6

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.1 - i

A: Given, To Evaluate, the complex number in trigonometric form with 0 ≤ θ < 2π.1 - i Here  a=1 and…

Q: (5-8) and (-31)

A:

Q: Write each complex number in standard form.   8(cos 330 degree + i sin 330 degree )

A:

Q: 3+4i 2i Simplify the expression to a single complex number:

A: We can solve the Complex number expression by using the technique of Complex conjugate . In the…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-17

A: Let z=−17⇒z=−17+i0The complex form z=x+iy in trigonometric form is written asz=rcosθ+isinθ,…

Q: Write each complex number in polar form. 1. −3 − 3i√3

A: Given that, z=-3-33i Write each complex number in polar form.

Q: (7-21) and (5 + 8i)

A: Find the distance between and the midpoint of each pair of complex number (7-2i) and (5+8i) .

Q: Write each complex number in standard form.       1 cis 240 degree

A: Consider the provided expression,   1 cis 240 degree  We can write as, cos240°+isin240°

Q: Write each complex number in standard form.     4(cos 30 degree +i sin 30 degree )

A: 4cos30°+isin30° We need to write the complex number in standard form

Q: Transform the complex number into its rectangular (1+5i)

A: (1+5i)

Q: the complex number 5 Cis 210 in standard form

A:

Q: Plot each complex number: 1. -3i 3 2. 1. -2 -1 5. -11 -2

A: In complex plane  z = x + iy    = (x,y)

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4√3 + 4i

A: Given: -4√3 + 4i Here  x=-43, y=4r=x2+y2=-432+42r=163+16=64r=8                        ... taking…

Q: Write each complex number in standard form.       1 cis 210 degree

A: Given: cis210° To convert the given complex number in standard form. Solution: cisθ is an…

Q: In Problem,write complex number in the standard form and plot each in the complex plane.

A: the given complex number in polar form is: 0.5cos160° +isin160° we have to write the given complex…

Q: Write the complex number in polar form with argument 0 between 0 and 27. -V6 + vzi

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.2 + i

A: Consider the provided information, 2+i  Express the complex number in trigonometric form with 0 ≤ θ…

Q: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a…

A: Given complex number 3-4i    Point can be taken as (x,y)=(3,-4)      r=√(X2+y2)    r =√(32+(-4)2)…

Q: find each of the products and express the answers in the standard form of a complex number. (5 - 3i…

A: The value of the given expression can be found by the square formula of difference. Apply the…

Q: Write the complex number in standard form.  2 cis 5

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Q: Find the distance between the complex numbers in the complex p 1 + 7i - 1 + 5i

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Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.2√3 + 2i

A:

Q: find each of the products and express the answers in the standard form of a complex number. (9 + 6i…

A: (9 + 6i ) (-1 - i )=9(-1-i)+6i(-1-i)                           =-9-9i-6i-6i2           distribute…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.4 + 5i

A: Given that, the complex number 4+i 5 Express the complex number in trigonometric form with 0 ≤ θ…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.2 - 2√3 i

A: Given complex number is: z=2-23i Let us consider, r cos θ=2r sin θ=-23 Then we get,…

Q: Use a calculator to help write each complex number in standard form. Round the numbersin your…

A: Given complex number, 10cos12°+isin12°

Q: Use de Moivre’s formula to find the Cartesian form of the complex number  (-2 + 2√3i)7

A:

Q: Write each complex number in trigonometric form. Round all angles to the nearest hun-dredth of a…

A: Given: -2-3i

Q: Use a calculator to help write each complex number in standard form. Round the numbersin your…

A: The complex number in the form a+ib , where  is real part and b is imginary part.

Q: Use a calculator to help write each complex number in standard form. Round the numbersin your…

A: Let z = 5(cos 70 degree + i sin 70 degree) The complex number z is in polar form: z = r(cos theta +…

Q: Match the correct modulus or absolute value to the complex number: - 6 + 8i

A: Explanation and solutions is given below....

Q: Write the complex number in standard form. 120(cos 7.5 + i sin 7.5)

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.3 + 2i

A: Here the given complex number z=x+iy=3+2i⇒x=3,⇒y=2

Q: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a…

A: Complex number in trigonometric form

Q: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a…

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-2 - 2i

A: Solution: Consider the given complex number is: z = -2 - 2i The trigonometric form of a complex…