1. Use De Moivre's Theorem to write the following complex number -6 Z = (-1+i)30 in Polar Form z = r(cos 0 + i sin 0) wherer is the modulus and 0 is the argument in radians.

Q: (a) For complex numbers z₁ = 6 + 6j and z₂ = 4 − 4j, π (i) find z = 21. Present your result in polar…

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Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. * False True

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Q: Prove the Euler's formula: e" = cos0+ jsin 0 using the definition of the complex number

A: We have to prove that ejθ=cosθ+jsinθ. We know that ex=1+x+x22!+x33!+x44!+.......... Now,…

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: Let z be a complex number. Then cos(5z)+i is bounded in C.* O False True

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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: 1. ________ Theorem states that if z = r(cos θ + i sin θ) is a complex number and n is a positive…

A: Given: 1. ________ Theorem states that if z=rcos θ+i sin θ is a complex number and n is a positive…

Q: Question 9: Given that z = cos+ i sin and u- iv = (1+z)(1 − j²z²). Show that 30 2 V = utan r = 4²…

A: For any queries please let me know through comments. I will try to reply ASAP! Please like if…

Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. O True O False

A: Use z=x+iy, then show it is bounded.

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

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Q: 3. Convert the Complex number 10V3- 10i to trigonometric form: r(cos(0) + i sin(0)). 4. Let z =…

A: I have Provided this answer in step-2.

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: 6. Determine the order of the following complex number! о( со COS 3 57 3 +i· sin 3 -

A: That's easy. Have a great day!!!

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

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Q: Let z be a complex number. Then cos(32)-i is unbounded in C. * False True

A: use:- cos(x+iy)=cosxcoshy−isinxsinhy

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

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Q: Write the complex number z = 18 + 18j in trigonometric form O 19.7(cos23.96°+ j sin 23.96°) O…

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

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Q: 6. Find the following complex numbers in the form r+ iy, whe and y are real. (i) (3+7i) + (6 – 10i)…

A: we have to find complex numbers in the form of x + i y  Adding real part with real part and…

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

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Q: Let z be a complex number. Then cos(7z)+3i is unbounded in C. * True False

A: From the question image that you have uploaded, only 1 complete question is visible, which is the…

Q: How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. a. (-z) b.…

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Q: Find the quotient z1/z2 of the complex numbers z1 = 50(cos 4π/3 + i sin 4π/3) and z2 = 5(cos π/3 + i…

A: Find the quotient z1/z2 of the complex numbers .

Q: Write the complex number z = (1+ v3 i)" in polar form: z = r(cos 0+ i sin 0) where

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

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Q: V3 1 (- 2

A: given(-32-12i)20 =(-1)20(32+12i)20 =(cos30+isin30)20 The formula of Demoivre's theorem is cos θ+isin…

Q: b) Given the complex number z = -V32 + V32i. i. Express z in polar form. Vz and sketch ii. Obtain…

A: ----------------------------------------------------- Given: z = -32 + 32iAim: To express 'z' in…

Q: Consider the following. Square roots of 5(cos 90° + i sin 90°) (a) Use the formula zk = V r cos- 0…

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Q: xpress the complex number z = -2i in polar prm r(cos 0 + i sin 0). elect the correct answer below: )…

A: Use polar coordinate to solve

Q: 6) Divide the complex numbers, and leave the result in polar form. 8(cos 100° + j sin 100°) 4(cos…

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Q: Q3. Given the complex numbers z1 = -V3 +i,z2 = 2 - i,z3 = -V3 – 3i and z4 = 4 + 4i 3.1 Represent the…

A: We have to solve given Questions

Q: The polar form of the complex number –3/3 + 3i is 6(cos(150°) + isen(150°)) 6(cos(300°) +…

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Q: Consider the following complex number. Z = 4(cos (280°) + i sin (280°)) (a) Find two square roots…

A: Root of complex number

Q: Given complex numbers z, and z,, 11π 11 t +i sin 4 11 t +i sin 12 11 T z, =3 Z2 =14 cos cos 4 12…

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Q: Let z be a complex number. Then cos(72)+3i is unbounded in C. False True

A: this is true , because

Q: 1 If a complex number z satisfies | -3 | z+3 find the largest %3D sin75 ° cos75°* Value of | z+i|.…

A: We are given that a complex number z satisfies z-3+z+3=1sin75∘ cos75∘ . So,…

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: Let z be a complex number. Then cos(72)+3i is unbounded in C. * O False True

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Q: Find all the complex square roots of w 9( cos 45° + i sin 45°). Write the roots in polar form with 0…

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Q: Express the complex number z = -V2 - V2i in polar form r(cos 0+i sin 0). Select the correct answer…

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Q: Let z be a complex number. Then cos(72)+3i is unbounded in C.

A: A complex no. in the form of a+ ib

Q: =(-1= v3i)³

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Q: Question 9: Given that z = cos + i sin and u- iv = (1 + z)(1 − j²z²). Show that V = utan 30 2 r = 4²…

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Q: 7. Find the product of the following complex numbers. Leave answer in polar form. z1 = 5(cos 20° + i…

A: Given, z1 = 5cos20°+isin20° z2 =4cos10°+isin10°   We have to find the product of the above two…

Q: Let z be a complex number. Then cos(tz)+3i is unbounded in C. * False True

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Q: 2(2) A complex number z = v2(cos+i sin ), find In ( Z.Z' )

A: z = √2(cosπ/4 + i sinπ/4)  z = √2(1/√2 +i/√2 )  z = (1+i)  z* = 1-i

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.