2. Do the following calculations (a) Write –V3 + i in polar form. (b) Find all 3rd roots of 8i. (c) Find ALL solutions of z2i = -1.

Q: 4. Consider the complex equation - -32i. (a) Solve for all values of z.

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Q: Find the 3 complex numbers z E C that satisfy the equation z³ = -27. Write the solutions in polar…

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Q: (a) Use the formula zk = Vr(co e+ 27tk cos +i sin 0+277K to find the indicated roots of the complex…

A: Given Z=-322(-1+i) Zk=rncosθ+2πkn+sinθ+2πkn, 0≤θ<2π The trigonometric form of the complex number…

Q: find polar form of the complex number Z= = (2√3-4i) + (-√3+5i).

A: The complex number: z=x+iy can be represented in its polar form as z=rcosθ+isinθ. Here, r=x2+y2,…

Q: Find the product of the complex numbers: z, = -V3+3i and z2 =1+ 2i in polar form.

A: Given:          z1=-3+3i          z2=1+2i         product of complex number =z1×z2…

Q: 2.1 Find the value of x and y from the given complex equation (-2+ i)x + 2y =1+ 3i. 2.2 Write the…

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Q: Express the given complex number in polar form. [1(cos(3)+ i sin()) [2(cos() + + sin(+))] ¹0 10

A: We know that eiθ=cosθ+isinθ and eiθn=einθ ∀n∈ℤ .

Q: (b) Given the equation z₁ = 1 + √3i, z₂ = −2 −2i. (i) Convert z, and z₂ into polar form. (ii) Hence…

A: Given the equation z1=1+3i, z2=-2-2i (i) To convert z1 and z2 into polar form. (ii) Hence, by using…

Q: 1. z3 = 8i 2. z4 = 2 – 3i 3. z2 = sin(1 + i)

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Q: Solve for the value of each of the complex variable in the following equation. Express your answers…

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Q: 2. Write the following complex numbers in polar form. (a) 2', (b) e-. 3. Prove the = e-" where z and…

A: Given that  2) a) 2i b) e-i 4) a) z5=1 b)5z2+2z+10=0

Q: Give the solutions of the complex equation –3z°(1 + i) = z(1 – i) in trigonometric for

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Q: If Z₁ = = 13 - 10i and Z₂ = = −15+ 9i, determine the following: 4z₁ - 5z₂ (Polar Form)

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Q: In((5+j3) + (6e12)] - 10430°

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Q: 1. Find all the roots in both polar and Cartesian form for each expression. (a) (-2+2i) (b) (-9i)?

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.