3. Let w = 3-3i and z= -2+2√3i. (a) Express w and z in polar exponential form. (b) Express (wz)10 in polar exponential form using the principal argument.

Q: (b) Show that i10 is real, even though i or 10i is not.

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Q: (b) Show that i³i is real, even though i or 3i is not.

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Q: 3. (a) The complex conjugate of 3  4i is 3  4i  .(b) 13  4i2 13  4i2  .

A: a) Complex conjugate of 3+4i is, By definition, For a complex number z=x+yi, its complex conjugate…

Q: Consider the complex number z = (1 – i)(-1-iv3). Find |2| and arg(2).

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Q: swer in polar form where r> 0 and

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Q: Find x and y if (-3x - 9) + 4i = 6 + (3y - 2)i.

A: Given that,  (-3x - 9) + 4i = 6 + (3y - 2)i To solve for x and y, need to use below property of…

Q: (5 – 6i) – (3 – 2i)

A: We have to perform the subtraction between two complex numbers.

Q: Multiply the following. - 5ab (xa° + ya - 2) - 5ab (xa° + ya - 2) =(Simplify your answer.) 6

A: Given the term is , - 5ab(xa⁶ +ya³ - 2)  We have to multiply the term and simplify it  First we have…

Q: . Subtract (3 – 2i) from (-2 + 3i), and express in a + bi form.

A: Here we sutract one complex no . to another complex no.

Q: Which of the following expressions simplify to 4x? y? (4xy) (4x) (&xy²) (2r°yz) y(2x²y)

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Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) -…

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Q: Q1- If z₁ =3+2i, and z2 = 1-2i. Fined the real part and imaginary part of the 2z2-z₁+5-i following…

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Q: Verify that (¹)² = i²i but that (i²)i ‡ į²i ("i" imaginary unit)

A: What is Complex Number: A real number and an imaginary number are effectively combined to create a…

Q: Write the complex number z=(1-√3i)2015/(√2cis(7π/6))4028 in an exponential form.

A: cis(x) = cos(x)+isin(x)

Q: -1+5i -i

A: topic- complex numbers  real part is added and subtracted with real part and imaginary part is added…

Q: (1 +i)(13 – 4i)(1 - i)

A: We have to simplify the given expression: 1+i13-4i1-i We know that a+ba-b=a2-b2i=-1i2=-1 Where, i is…

Q: Solve using complex analysis: 1²t Jo 5-4cos(0) 2 cos(30) -do

A: Given: ∫02πcos3θ5-4cosθdθ. We have to solve using complex analysis.

Q: 5. Find all the roots in both polar and Cartesian form for each expression. (a) (-2+2i) *. (b) (-1)…

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Q: Write the standard form of the complex number 4(cos(4π÷3)+isin(4π÷3)    Find the product:…

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Q: If z1 =3 - 5i and z2 =26 -2i, find z1 +z2 and z1 -z2.

A: Given that, z1 = 3 - 5i z2 = 26 -2i We have to find z1 + z2 and z1 - z2.

Q: Simplify the complex number 7 (²+1) ³ - 5 (¹)² and express it in the standard form.

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