Convert the complex number –4 – 9i into polar form. Express the angle using degrees over the interval 0° <0 < 360°. You may round the argument to the nearest tenth of a degree (if necessary), but you must express your modulus in it's exact form.

Q: Find all the complex roots of 125(cos 165° + i sin 165°). Write roots in polar form with θ in…

A: Given: The complex number 125(cos 165° + i sin 165°).

Q: Write the complex number 4 COS 7π 4 7π + i sin 4 in the form a + bi.

A: Complex numbers is given in form of a+bi.

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

A: Given complex number z = -5 + 5√3i.Graph the complex number.

Q: 12 TT CoS + i sin + i sin 6.

A: I am attaching image so that you understand each and every step.

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

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

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

A: Solution :-

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

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

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Q: Find the indicated powers of the given complex number. Express the result in polar form, then…

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

A: Given:     Z = 3ei(4π/3)

Q: Write the complex number in trigonometric form r(cos 0+i sin 0), with e in 5.3+5i 10(cos 60° + i sin…

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Q: Given the complex numbers z1 = 5 (cos(92°) + i sin(92°)) and z2 = 2 (cos(-92°)+i sin(-92°)), find…

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Q: Find the product of the complex numbers z1 = 6(cos 20° + i sin 20°) and z2 = 5(cos 50° + i sin 50°).…

A: the givn complex numbers are: z1=6(cos20°+isin20°)z2=5(cos50°+isin50°)

Q: Convert the given polar complex numbers into (a + jb) form giving answers correct to 4 significant…

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Q: Obtain the complex number cos (1 + i).

A: See the detailed solution below.

Q: Write the complex number z = 1 + I square root of 3 in polar form with the angle in degrees.

A: given,         z=1+3i

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

A: Given : two complex numbers as  z1=20cos75°+isin75°z2=4cos25°+isin25° To find : The quotient z1z2.…

Q: Rewrite the complex number 5(cos5.5+i sin5.5) in a+bi form

A: See the details solution below

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 given complex number in polar and rectangular forms. 10.0 e 1.20j

A: We have to write polar and rectangular form of given complex number:

Q: 11 Convert the complex number 8( cos 11T + i sin to polar form. Give exact answers for r and 0 (no…

A: Given :- Polar form, 8(cos(11π/6) + i sin(11π/6))   where, θ = 11π/6 and r = 8   = 8(cos(11π/6) + i…

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

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Q: Make this compley number in polar Form: Z - 5 +V4 i 5-6i

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Q: The complex number (cos+ i sin can be expressed in the form a + bi, where a, be R, as 31. COS 27 27…

A: solution:-

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

A: The given complex number is, 1+i12. The objective is to change the given complex number to the form…

Q: Find the standard form of the complex number 6(cos 17°26' + isin 17°26'). Round values to the…

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Q: Find the product of the complex numbers z1 = 4(cos 50° + i sin 50°) and z2 =  7(cos 100° + i sin…

A: Given complex numbers - z1 = 4cos50°+isin50°                ..........................(1)z2 =…

Q: Express the complex number z = -6/3 – 6i in polar form r(cos 0+ i sin 0). Provide your answer below:…

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

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Q: Put the complex number of (1+2i)/(2+i) in the form if a +bi, where a and b are real numbers

A: The given complex number is 1+2i2+i.

Q: Express the following complex number in its polar form. 2+5i -4-7i .i'(V3 – i10)(2 – i5)

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

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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: Find all the complex fourth roots of 16(cos 120° + i sin 120°). Write roots in polar form, with θ in…

A: z=16cos120°+isin120°

Q: Use a scientific calculator or unit circle to convert the polar form of the complex number to its…

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Q: Evaluate the given complex number: 3i (4 – 5i) (6 cos 25° + 6i sin 25°) and determine the modulus…

A: The complex number z=x+iy in its polar form can be written as z=rcosθ+isinθ. Here, the modulus,…

Q: Write the given complex number in polar form and in then in the form a + ib. You may use the De…

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Q: a) -4 – 7i to polar form b) 2.5 cis- to Cartesian form 9

A: a) Given the complex number, z=-4-7i Then, r=z=42+72=65 Also, θ=tan-1yx=tan-1-7-4=60.255° Then, the…

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: Express the given complex number in polar form z=-5*square root of 3 - 5i)

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Q: Convert the given complex number from rectangular to polar form. - 3/2 +3j/2 - 3-/2 + 3j/2 =(cos +…

A: We have to find

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

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Q: Write the complex number in polar form with argument θ between 0 and 2π. 8 − 8i

A: To determine the polar form of the complex number.

Q: Write the complex number in polar form with argument e between 0 and 2N. 6 + 6V3i

A: We have to find the polar form

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.