Plot the following complex numbers z = 6 – 3i and w = 2 + 5i and find the midpoint of the line segment formed.

Q: Write the following complex numbers in the trigonometric form r(cos0+isin 0) with 0 (exact) in…

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Q: Q2/ Write the complex number 5(cos+i sin) in its rectangular form and then plot it in the complex…

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Q: To convert a complex number from rectangular form, z = a + bi, to polar form, z = r(cos e + i sin…

A: We fill the blank spaces as,

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

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Q: Write the complex number 0.6(cos 100° + i sin 100°)in rectangular form. If necessary, round to the…

A: The given complex number is 0.6cos100°+isin100°.

Q: Find the polar form of the following complex numbers: (a.) z1 = 1+iv3, (b.) 22 = -2 + 2i, (с.) 23 —…

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Q: Write the complex number 5(cos π/2 + i sin π/2) in rectangular form. If necessary, round to the…

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Q: Add the following two complex numbers: (3 + 2i) + (5 – 31). What do you notice?

A: Given that (3+2i)+(5-3i)

Q: Express the following complex number in its polar form. i"(V3 - i10)(2 – 15)

A: The given problem is to evaluate and simplify the given complex expression and express in the form…

Q: Find the complex trigonometric form of Z =-2i

A: Trigonometric Question

Q: For the complex numbers w = 81cos 40° + i sin 40°2 and z = 21cos 10° + i sin 10°2, find each of the…

A: (a) part Consider the given complex numbers w=81cos 40°+i sin 40°z=21cos 10°+i sin 10° Since, the…

Q: Write the following complex number in Polar form: 5+ V4 i Z = 5-6i

A: At first, we will remove the i from the denominator. Then we can write polar form as z = r(cosθ +…

Q: Write the complex number 4(cos 210° + i sin 210°) in rectangular form. If necessary, round to the…

A: Given that: The complex number 4(cos 2100 + i sin 2100) To write the given complex number in…

Q: First simplify each of the following numbers to the r + iy form or to the re“ form. Then plot the…

A: Given, 11+i Divide and multiply 1-i  ⇒11-i1+i1-ia-ba+b=a2-b2⇒1-i12-i2

Q: Find a motion that moves the line x + 2y = 3 to the y-axis and point (1,1) to the origin. Give the…

A: We need to find the motion which moves the line x+2y=3 to the y-axis and the point (1,1) to the…

Q: Write the complex number 4(cos 5π/6 + i sin 5π/6) in rectangular form. If necessary, round to the…

A: 4cos5π6+i·sin5π6

Q: Find a motion that moves the line x + 2y = 3 to the y-axis and point (1, 1) to the origin. Give the…

A: To find a motion that moves the line x+2y=3 to the y-axis and the point 1,1 to the origin i.e.0,0.…

Q: Write the complex number 8(cos 60° + i sin 60°)in rectangular form. If necessary, round to the…

A: 8cos60°+isin60°

Q: Perform the indicated operation and express the result as a simplified complex number. (5 + 7i) (4 –…

A: We have to simplify the following complex number -  (5+7i)(4-i)

Q: Write the complex number 6(cos 30° + i sin 30°) in rectangular form. If necessary, round to the…

A: Given:  6cos30°+isin30°sin30°=12cos30°=32

Q: perform the indicated operation and express the result as a simplified complex number 3+7i/i

A: To simplify the given problem. (3 +7i)/i

Q: Write the following complex numbers in the trigonometric form r(cos0+i sin 0) with 0 (exact) in…

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Q: Find the Real and Imaginary Part of 1+sqrt(3i) and plot it in the complex plane

A: Complex number of form z = x+yi Where, x is real part and y is imaginary part

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: To convert a complex number z = x + yi from standard form into trigono metricform, use the…

A: The modulus of a complex number z=x+yi is r=x2+y2 & the amplitude or argument is,…

Q: Add the following two complex numbers: (3 + 2i) + (5 – 3i). What do you notice?

A: Add the following two complex numbers: (3+2i) + (5-3i)

Q: Write the complex number 8(cos 7π/4 + i sin 7π/4) in rectangular form. If necessary, round to the…

A: Explanation: Given that,  Complex number in polar form: 8cos7π4+isin7π4 Convert it into a…

Q: Write the complex number 30(cos 2.3 + i sin 2.3) in rectangular form. If necessary, round to the…

A: the given complex number is 30cos 2.3 +isin 2.3. we have to write the complex number in rectangular…

Q: Combine the following complex numbers [(3 + 3i) − (5 + i)] + (4 + i)

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Q: In calculus, it can be shown that eiθ = cos θ + i sin θ. Use this result to plot the complex number…

A: Given:eiθ=cosθ +i sinθWe have to plot the graph of the complex number-e-πi

Q: Take the last four digits ABCD of your student identification number, and let z1 = A + Bi and z2 = C…

A: We will be taking the last 4 digits as ABCD. Let z1 = A + Bi and z2 = C + Di be the corresponding…

Q: First simplify each of the following numbers to the  x+iy form or to the re^i teta. Then plot the…

A: The given complex number is i-4. Simplify the given complex number as follows. i-4=1i4=11…

Q: Write the complex number 20(cos 205° + i sin 205°) in rectangular form. If necessary, round to the…

A: Our Aim is to write the complex number 20[cos(205°)  + i sin(205° )] -(i)in rectangular form.

Q: Write the following complex number in Polar form: 5+ va i z = 5-6i

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Q: Simplify the complex numbers and express your final answer in polar form z = r(cos0 + isin0):

A: Complex number in polar form…

Q: Find the indicated powers of the given complex number. Express the result in polar form, then…

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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: Find all the complex cube roots of w = 8( cos 270° + i sin 270°). Write the roots in polar form with…

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Q: Write the following complex number in Polar form: 5+ V4i Z= 5-6i

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Q: Write the complex number 4(cos 240° + i sin 240°) in rectangular form. If necessary, round to the…

A: Given: 4(cos 240°+i sin 240°) can be expressed in the Euler's…

Q: Write the complex number 7(cos 3π/2 + i sin 3π/2) in rectangular form. If necessary, round to the…

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Q: Write the complex number 12(cos 60° + i sin 60°) in rectangular form. If necessary, round to the…

A: Given:12cos 60° + i sin60°

Q: Write the following complex number in Cartesian, Polar and Exponential form. V2 + V6i -1+ V3i

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the quotient and write the result in standard complex form: 4. (cos 250° + i sin 250°) 7. (cos…

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Q: Use this result eiθ = cosθ + i sinθ to plot the complex number.

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