write the given complex number in polar form and in then in the form a + ib. +isin 8. 8. 8 cos 10 [2 (cos- +i sin ) 16 16.

Q: Write the following complex numbers in the trigonometric form r(cos0+isin 0) with 0 (exact) in [0°,…

A: 1(a). The given complex number is: z1=12-12i

Q: 5.) Find the complex cube roots of: 8(cos 60° +i sin 60°). (write them allI)

A: We use De moivre's theorem

Q: Find the polar form of the following complex numbers: (a.) z1 = 1+iv3, (b.) 22 = -2 + 2i, (с.) 23 —…

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Q: 1. Convert the following Complex Numbers into Polar and Exponential Form V3 + a) 2_ b) V3 – ü

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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: Express the complex number z = -6i in polar form r(cos 0 + i sin 0). Select the correct answer…

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Q: 1. Find each of the following. Write each complex number in the form x+ iy. (a) Write (-2 – i) in…

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Q: Rewrite the complex number 3(cos 3.5 + i sin 3.5) in a + bi form a = b =

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Q: Put the following complex number 1 3 3 3 into polar form. Choose the correct answer from the…

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Q: Determine the polar form of the complex number 5 – 3i. Express the angle e in degrees, where os es…

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Q: Write each complex number in complex polar notation: 26.7 X (4.053 + 2.042 i) = (4.53 (4.482 + 4.681…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: If Z=a+2i is a complex number, the fundamental value of its amplitude 5TT/6.find the value of a and…

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Q: In this question we use the complex numbers x = 1 + 2i, y = 3-i, 3π 3π √2(cos ³4+ isin ³7). Complete…

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Q: 30. The complex number 1 + V3i can be expressed in exponential form as 2e A в 2e- is 2e- 2e D

A: In the given question we have to expressed the complex number z in the exponential form…

Q: 5. ) If 3x + 4yi = z2, what is x+y equal to?

A: We know that Euler's formula  e^(ix) = cos(x) + i sin(x)

Q: determine the indicated roots of the given complex number.   (2(cos π/3 + i sin π/3))1/2

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Q: 5+ V4 i Z = 5-6і

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

A: See the details solution below

Q: Evaluate the given complex number. z=[tan(1-i)]^[cot(1+i)]

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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 following complex numbers in the form a + bi, a. 5(cos 0° + i sin 0º) b. 2(cos 30° + i…

A: A complex number is of the form a+ib  where,   real part is a and,  b is imaginary part of the…

Q: Find three cube roots for the following complex number.    27(cos 120° + i sin 120°)   w0= w1= w2=

A: We find out three cube roots of given complex number using z1/3=r1/3(cos…

Q: Express the complex number z = 4 – 4/3i in polar form r(cos 0 + i sin 0). Select the correct answer…

A: Given: z=4-43i

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: ne following: The polar form of a complex number z=a+ bi is given by z=r(cos0+ isino), where ris the…

A: This is the question of complex numbers.

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: Write the standard form of the complex number.  7/6 (cos 5pi/6 + i sin 5pi/6)

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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: (5) represent the Following in Polar form (a) -5 +5i (b) -ro- Jz i (C) - 3? |

A: We need to represent the following polar form: (i) -5+5i(ii)-6-2i(iii) -3i Since we are suppose to…

Q: 6. Express each complex number in polar form. a) 13+3i d) 16.2–12/3i b) -19+9i e) 14 +9i 3 1 c) -23-…

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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: Represent the following complex numbers in polar notation;  a) z=−5+5i

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Q: 20) Write the complex number in rectangular form. 5(cos 195° + j sin 195 °)

A: The given complex number is 5(cos195°+j sin195°). The objective is to find the rectangular form of…

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

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Q: Express the following complex numbers in the form of re". a) z=-1-3i b) p=| 4(cos - i sin ") 3 3 c)…

A: Using exponential form.   As per our guidelines we are supposed to answer?️ only first 3 question.…

Q: express the given complex number in polar form R(cos θ + i sin θ) = Reiθ.  √3−i

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Q: The value √(a2 + b2) is the_______ of the complex number a + bi.

A: Solution:-  The value a2+b2 is the_______ of the complex number a + bi

Q: Find the product of the given complex numbers in polar form. 3 (cos +i sin 푸).4 (cos (-표) + isin…

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Q: Given the complex number w = 4(cos 110° + i sin 110°). Compute the following, leaving your answer in…

A: formula : if then Given :

Q: CONVERT THE GIVEN COMPLEX NUMBERS: 1. A = 6+7i POLAR FORM 2. B = 5230 → RECTANGULAR FORM 3. C = 15 –…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: 4. Multiply and Divide the following complex numbers, give your answers in rectangular form z = 12…

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Q: Derive the formula for the cos-1(z), where z is a complex number.

A: With the current notation of the question, the question probably wants us to derive a formula for…

Q: Z1 = 2 + 4i Z2 = 5e2i %3D Z3 = 4 cis 40°

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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: 4. The complex numbers u and v are as follows: u = 3cis(1.234) and v = 2cis(2.415). Write the…

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Q: 3. Símplify to a complex number: 3 + 6i 3i

A: Given, complex number = 3+6i3i   We have to simplify the complex number

Q: Write the complex number z = -10 + 10i in polar form: z = r(cos 0 +i sin 0) where and 0 = ... The…

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Q: 2. What is the standard form of the complex number –13.5(cos() + i sin())?

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Q: z = sin(e³) + sinh(5230°)

A: