In Exercises 11-26, plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. 11. 2 + 2i 12. 1 + iV3 13. —1 — і 14. 2 - 2i 15. -4i 16. -3і 17. 2V3 - 2i 18. -2 + 2iV3 20. -4 22. 3V2 - 3iV2 19. -3 21. –3V2 - 31V3 23. -3 + 4i 24. -2 + 3i 25. 2 – iV3 26. 1 - iV5

Q: Write the complex number in standard form. 8 cis (210°)=___+___i

A: We need to write the complex number in standard form. Here,                  8 cis (210°)=8 cos 210°…

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: For Exercises 41-42, find the indicated complex roots. Write the results in polar form using degree…

A: 41. Consider the square root of 25cos120°+isin120°. If z=rcosθ+isinθ is the given complex number in…

Q: Find the quotient of the complex numbers. Leave your answer in polar form. Express the argument as…

A: Write Z1 and Z2 in form of e^i*theta

Q: Need help

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Q: Write the complex number in polar form with argument 0 between 0 and 2n. 7 - 7i

A: The expression of the polar form is given by z=rcosθ+isinθ Given complex number is (x+iy)=7-7i. The…

Q: In Exercises 78–81, find all the complex roots. Write roots in rectangular form. 78. The complex…

A: Given: 78. 16cos2π3+i sin2π3 79. 8i 80.-1

Q: Let z be a complex number, and w be its additive inverse. Let c be another complex number. If |zc| =…

A: Given z be a complex number and let w be its additive inverse. ⇒z+w=0 and z=w, argz=argw+π Given…

Q: write the standard form of the complex number 7/4(cos(3pi/4)+isin(3pi/4))

A: Here cos3π4=cosπ-π4                =-cosπ4                =-12 sin3π4=sinπ-π4               =sinπ4…

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

A: Given: Let z=-1+i8  To Find: To change the given complex number into a+ib form using De Moivre’s…

Q: Find the modulus and argument of the complex number (2+i/3-i)2. Also express -5+ 5i in polar form

A: 2+i3-i2=2+i3-i·3+i3+i2=6+2i+3i+i29-i22=6+5i+-19--12=5+5i102=25+50i+25i2100=25+50i+25-1100=50i100=i2=…

Q: In Exercises 57-60, plot each complex number. Then write the complex number in polar form. You may…

A: Given: 57. 1-i 58.-23+2i 59.-3-4i

Q: 26. Use a calculator to help write the complex number in standard form. Round the numbers in your…

A: Solution: The objective is to write the given complex number in standard form

Q: What is the argument of the complex number given by z = (1+ iv3)(1 + i)(cos(0) + isin(0)) Select…

A: We have to find argument.

Q: Let and z2 be the complex numbers given in the following argand diagram. Find the complex number Z1…

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

A: Given that, 2+23i10

Q: 2. Write the number (2 – i)(-1+3i)(3 – 4i) in the form of +bi .

A: The detailed solution is as follows below:

Q: Write the expression complex number in standard form. as a 1) (-8 + 8i) – (2 + 4i) 2) (8i) + (-4 -…

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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: Find the conjugate, argument and modulus of the complex number Z=1+i3

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Q: In Exercises 61-64, write each complex number in rectangular form. If necessary, round to the…

A: 61). To write the complex number in rectangular form: 8cos60°+isin60° Solution: Given number can be…

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

A: 1-i10 Consider, z=1-i Now, z=12+-12=2 & θ=tan-1yx=tan-1-11=2π-tan-11     ∵The complex number 1-i…

Q: The complex number (−9+7i)/(9+5i) rewritten in Cartesian form is?

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Q: Write the complex number in polar form. Express the argument in degrees, rounded to the nearest…

A: In polar form z = r ei(theta) = r (cos(theta) + i sin(theta))

Q: Write complex number in standard form Z=3(cos240+i sin240)

A: To write given complex number in standard form, substitute the value of  and:

Q: Write the complex number in polar form with argument 6 between 0 and 2n. 9 + 9/3i

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Q: Use a calculator to perform the indicated operation. Give the answer in rectangular form. 2 cis 9

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Q: Present complex number z in algebraic form =* + 23D 35 1-3i

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Q: In calculus, it can be shown that = cos 0 + i sin 6. In Exercises 87-90, use this result to plot…

A: Since your question has multiple questions we have solved the first question for you.   Plot the…

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

A: 3+3i5 Consider, z=3+3i Now, z=32+32=32&θ=tan-1yx=tan-133=tan-11=π4 Now trigonometric form is,…

Q: If u and vare complex numbers such that u = 3 – 5i and v= -6 + i, which of the following is…

A: Given u = 3 - 5i   and   v = -6 + i

Q: -1 - V3i

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Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form

Q: 1. Write the complex number 2 + iv3 in the form of rei0

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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: Use De Moivre's Theorem to find the complex number raised to a power. Leave your answer in CIS form.…

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Q: Find the modulus, Izl, and argument, 8, of the complex number. -1+i One charaes 4.6

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Q: Write the complex number in polar form. Express the argument in degrees, rounded to the nearest…

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

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Q: 1. Write the complex number i+= in the form of rele V3

A: The polar form of complex number  is    , where     and  and .

Q: begin by sketching the argument 8 Write the complex number in trigonometric form the graph. . to…

A: A complex number is any number that can be written in the form a+bi where a and b are real numbers,…

Q: In Exercises 1–4, write the complex number instandard form.1. 6 + √−4 2. 3 − √−253. i2 + 3i 4. −5i +…

A: We have to write the complex numbers in standard form: 1. 6+-42. 3--253. i2+3i4. -5i+i2 We know that…

Q: Write the complex number in polar form. Express the argument in radians. 2- 2i O 22 cos +i sin 0 2…

A: Given problem:- Write the complex number in polar form. Express the argument in radians. 2-2i

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

A: Solution: Consider the given complex number is: z = 3 + i7 We have  z = a + ib⇒z = rcos θ + i sin θ…

Q: What is the first step in writing the complex number -1 + i in trigonomet-ric form?

A: Consider z=x+iy is any complex number, so polar form is, z=x+iy=rcosθ+isinθWherer=x2+y2θ=π-tan-1yx…

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

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

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

Q: Is O can be represented as a complex number? Select the correct response: True False

A: Is 0 can be represented as complex number .