Write the complex number z = (-1 - (3)1/3i)16 in polar form: z = r(cosθ + isinθ). The angle should satisfy 0 ≤ θ < 2π.

Q: Find the quotient z1/z2 of the complex numbers z1 = 2 - 2i and z2 = 1 - i. Leave answers in polar…

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Q: Find the polar form for the complex number -2-3i.

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Q: Simplify and convert into polar and exponential form of complex number: 2-3i 3+4i

A: Given complex number: z=2-3i3+4i   Write the given complex number into a + bi form to simplify.

Q: Write the complex number in polar form with argument 0 between 0 and 2n. -1 - V3i

A: Given query is to write the expression in Polar form.

Q: Write the complex number in polar form with argument 0 between 0 and 27. -V2 + Või

A: Given,         -2+6iWe know that,          The polar form of a compex number is given by…

Q: Convert the complex number to rectangular form. 8( cos 1 +i sin 1-π) 6

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Q: Find the quotient z1/z2 of the complex numbers z1 = 12(cos 3π/4 + i sin3π/4) and z2 = 4(cos π/4 + i…

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Q: Plot the number 1 + 2i on the complex plane.

A: 1+2i has the real part 1 and imaginary part 2. As the x-axis represents the real part and the y-axis…

Q: Write the complex number -V3 + i in trigonometric (or polar form) with 0 < 0 < 2n.

A: Using z= r(cos theta +i sin theta)

Q: Write the complex number in trigonometric form r(cos 0 + i sin 0), with 0 in the interval [0°,360°,

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Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-12i

A: Consider the complex number  −12i

Q: Express the complex number -2i in the form R(cos(0) + i sin(0)) = Re where R> 0 and 0 ≤ 0 ≤ 2. NOTE:…

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Q: Write the complex number z = 1 + I square root of 3 in polar form with the angle in degrees.

A: given,         z=1+3i

Q: Vrite the complex number in rectangular form. 7) COS + i sin - 6.

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Q: Find the midpoint between the pair of complex numbers. (-5 - 8i) and (-3i) O 2.5 + 2. 5i O-2.5 5. 5i…

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Q: Convert the polar form of the complex number to rectangular form . -2(cos(플) + isin(쫄))

A: Rectangular form x+jy Polar form r∠Θ r= √(x2 +y2 )  Θ= tan-1 (y/x)

Q: (A) Simplify the complex number z and express it both in rectangular and polar form. (3 + j6)(6+ j4)…

A: It can be calculated as given below:_

Q: Plot the complex number z = 3 + 2i and find its absolute value.

A: Consider the provided complex number, z=3+2i Find its absolute value. The absolute value of a…

Q: b) Express the complex number in polar form -4 + 4i

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Q: 12. Write the complex number -4 + 4i in polar and exponer

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Q: Write the complex number z= 5(cos+i sin) in its rectangular form and then plot it in the complex…

A: Given complex number, z=5cosπ3+i sinπ3 To find its rectangular form.

Q: (15) For the complex number z = ti find z2 by a) directly multiplying in the rectangular form given,…

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Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-4√3 + 4i

A: Given: -4√3 + 4i Here  x=-43, y=4r=x2+y2=-432+42r=163+16=64r=8                        ... taking…

Q: OConvert the complex number 2+i3 to polar form.

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Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-20i

A: -20i

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.2 + i

A: Consider the provided information, 2+i  Express the complex number in trigonometric form with 0 ≤ θ…

Q: The real part of the complex number z = (2+2i)² + e¹+2i is

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Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form. z1 = 10(cos 10° + i sin…

A: We have given complex numbers z1 = 10(cos 10∘ + i sin 10∘)z2= 5(cos 5∘ + i sin 5∘) We have to find…

Q: (1) |z + 3 + 4i| = |z − 5| (2) |z| = 4   Find all complex numbers z that satisfy both (1) and (2)…

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Q: Plot the complex number z = 4i and find its absolute value.

A: To plot the complex number z=4i and find its absolute value.

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.2√3 + 2i

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Q: Plot the complex number z = 4 - i and find its absolute value.

A: In the Argand plane, the real axis is the x-axis and the imaginary axis is the y-axis. The absolute…

Q: Express the complex number z = - 1 - (square root 3)i in polar form: Z = r ( cos ( θ ) + i sin ( θ )…

A: Explained below

Q: Let the left complex number be z1 and the right complex number be z2. +i sin- 43 - 4i 8 cos a) Write…

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Q: Plot the complex number z = 3i and find its absolute value.

A: Plot the complex number z = 3i and find its absolute value.

Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: What is the real part of the complex number z= -1 + √3i/2

A: Compare with complex number

Q: What is the result of multiplication of complex numbers -V3 + i and (cos + i sin .)? 57

A: Given complex numbers are -3+i, 18cos5π3+isin5π3

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.4 - 3i

A: Given: z=4-3i We know that any given complex numberz=a+ib can be written in polar form as below…

Q: Find the complex conjugate of (2+3i)/(1-i)

A: We find complex conjugate of (2+3i)/(1-i)

Q: What is the polar form of the complex number z = 3i? Z.

A: Given that z = 3i and find that what is the polar form of this . Here i attached solution of this…

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.3 - 3√3i

A: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.3 - 3√3i = 3 (1 - √3i) Multiply…

Q: Convert the complex number 4(cos(30°) + j sin(30°)) = Z from trigonometric form to rectangular form.…

A: The trigonometric form for a complex number is : z=r(cos θ+ jsin θ) . The rectangular form for a…

Q: Express the complex number -3+/4 in the polar form.

A: Complex number in polar form.

Q: =(-1= v3i)³

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Q: Write the complex number in trigonometric form r(cosθ+isinθ) with θ in the interval [0°,360°). 2+2i

A: Given complex number 2+2i. The objective is to write the complex number in the form  r(cosθ+isinθ).