Find the trigonometric form of each complex number of 32i and then find the fifth roots.

Q: Solve the following  complex numbers in their rectangular form. Use 4 decimal places  for the…

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

Q: Graph each complex number along with its opposite and conjugate.       2-i

A: A complex number is written in the form, z=a+bi where, a is the real part and b is the imaginary…

Q: Find the complex fifth roots of 32. Write roots in rectangular form. If necessary, round to the…

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Q: Find the complex fifth roots of -1 + i. Write roots in rectangular form. If necessary, round to the…

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Q: Find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest…

A: To find the complex fourth roots of 81cos4π3+isin4π3. Solution: We know that if z=rcosθ+isinθ is a…

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: find each of the following quotients, and express the answers in the standard form of a complex…

A: Given expression is 4i5+2i. To express the answer in the standard form of a complex number.…

Q: find each of the products and express the answers in the standard form of a complex number. (3i ) (2…

A: We have   3i(2 - 5i)To find the value of this , we simplify this as follows (3i)(2- 5i)  = (3i)(2) -…

Q: Find two square roots of each of the following complex number.   3 - 4i

A: Given complex number: 3-4i The square root of a complex number is as 3-4i Now, consider 3-4i=x+iy

Q: Graph each of the following complex numbers, and express each in trigonometric form.     √3+i

A: 3+i Comparing with x+iy, we get x=3  &  y=1 Now, r=x2+y2=32+12=3+1=2&θ=tan-1yx=tan-113=π6…

Q: Write each complex number in trigonometric form. In each case begin by sketch- ing the graph to help…

A: It has only x term which lies on 2nd quadrant.

Q: Write each complex number in trigonometric form, once using degrees and once usingradians. In each…

A: We have, z=5+5i On solving further, we get the result as z=51+iz=5212+i2z=5212+12iz=52cos45°+isin45°…

Q: determine the indicated roots of the given complex number.   11/3

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Q: Graph each complex number: 2 + 4i, -2 - 4i, and 2 - 4i.

A: Given the complex numbers: 2+4i, -2-4i and 2-4i

Q: find each of the following quotients, and express the answers in the standard form of a complex…

A: Our Aim isto simplify the expression given below:-6i-23i-(i)

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

A: 8cos60°+isin60°

Q: Write each complex number in standard form.     4(cos 30 degree +i sin 30 degree )

A: 4cos30°+isin30° We need to write the complex number in standard form

Q: Write each complex number in trigonometric form, once using degrees and once usingradians. In each…

A: The given complex number is 8i.

Q: find each of the following quotients, and express the answers in the standard form of a complex…

A: given complex number-4-7i6i,let z=-4-7i and w=6iz/w=-1.1667+0.667i

Q: find each of the products and express the answers in the standard form of a complex number. (6 - 2i…

A: We find the standard form of the product as,

Q: Graph each complex number. In each case, give the absolute value of the number.        -3-4i

A: We know that, complex numbers can be represented on the coordinate plane by mapping the real part to…

Q: Write each complex number in trigonometric form, once using degrees and once usingradians. In each…

A: If a complex number is defined as z=a+ib, then its trigonometric form is: z=rcosθ+isinθ…

Q: Solve the following  complex numbers in their rectangular form. Use the given formula and use 4…

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Q: find each of the following quotients, and express the answers in the standard form of a complex…

A: To express the complex number in standard form.(5+i)(2+9i) Solution: (5+i)(2+9i) On simplifying…

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: find each of the products and express the answers in the standard form of a complex number. (9 + 6i…

A: (9 + 6i ) (-1 - i )=9(-1-i)+6i(-1-i)                           =-9-9i-6i-6i2           distribute…

Q: find each of the products and express the answers in the standard form of a complex number. (7i )…

A: The standard form of a complex number is: z=a+ib Where,  a and b both are the real numbers. a is…

Q: Find the four complex fourth roots of -16i. Write answers in trigonometric form.

A: Given: z=−16i

Q: find each of the products and express the answers in the standard form of a complex number. (-6i…

A: find each of the products and express the answers in the standard form of a complex number. (-6i…

Q: Find the trigonometric form for the following complex number  -√3 + i

A: (- √3 + i )    =  2( ( - √3/2) + i*( 1/2 ) )    We know that, a complex number is always denoted as…

Q: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a…

A: The complex number is -8+6i.

Q: Write each complex number in trigonometric form. Round all angles to the nearest hun-dredth of a…

A: Given: -2-3i

Q: Write each complex number in trigonometric form.      -5i

A: We have complex number -5i This complex number lies to complex number line and argument of this…

Q: Solve the following  complex numbers in their rectangular form. Use 4 decimal places  for the…

A:

Q: Find the square roots of the given complex number by using result (10) and then confirm the result…

A: We can find the square root of complex number by using the formula.

Q: Find the three cube roots for each of the following complex numbers. Leave your answersin…

A: Consider the complex number: z=8cos 210°+i sin 210°. Find the cube root that is, z13=8cos 210°+i sin…

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: find each of the following quotients, and express the answers in the standard form of a complex…

A: Given 3i2+4i

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: Find the complex fifth roots of 32(cos 5π/3 + i sin 5π/3). Write roots in rectangular form. If…

A: Given: z=32cos5π3+i sin5π3.