Express the following complex numbers in the form a + bi, a. 5(cos 0° + i sin 0º) b. 2(cos 30° + i sin 30°) c. V(2) (cos 45° + i sin 45°) d. V(3) (cos 60° + i sin 60°) e. 3(cos 90° + i sin 90°)

Q: Find the product of the two complex numbers. 21 = 3 (cos 10 +i sin 10") and zg=-2(cos 35" +i sin…

A: Given: x1=3(cos 10°+i sin10°) and x2=-2(cos 35°+i sin 35°)

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

A: 1(a). The given complex number is: z1=12-12i

Q: Find the magnitude of the resulting complex number, 6 (cos 120°+i sin 120°) x 4(cos 30° +i sin 30°)

A:

Q: 12 TT CoS + i sin + i sin 6.

A: I am attaching image so that you understand each and every step.

Q: Express the complex number in exact simplified rectangular form.

A:

Q: Rewrite the complex number 3(cos 3.5 + i sin 3.5) in a + bi form a = b =

A:

Q: Express the following complex number in its polar form. 2+5i 6.- -4-7i

A: Solution :-

Q: z2 + (3 – 2i)z + (2 + i) = 0

A: Here, we need to solve the following complex number equation.                 z2+(3-2i)z+(2+i)=0 Let…

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: Express the following complex number in the form x + iy respectively 3em/2

A: The given complex number is 3eiπ2. Write the given complex number in the standard form.…

Q: Use the trigonometric form of a complex number to show that z-n = 1/zn , where n is a positive…

A: To prove the given identity

Q: Given the complex numbers z1 = 5 (cos(92°) + i sin(92°)) and z2 = 2 (cos(-92°)+i sin(-92°)), find…

A:

Q: Express the following complex numbers in the form re : i. 3 + Ti ii. 25 - 1/Tti iii. (i+ 1)T

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: Solve the following complex numbers: Z1 = 5+3i ; Z2 = 4+5i ; Z3 = 3-i %3D

A: Givenz1=5+3i ; z2=4+5i ; z3=3-i

Q: Rewrite the complex number 5(cos5.5+i sin5.5) in a+bi form

A: See the details solution below

Q: Represent the following complex numbers in polar notation; a) z=−4 b)z=−5+5i

A:

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

A:

Q: i7(√3-i10) (2 - i5)

A:

Q: Express the following complex number in its polar form. 2+5i -4-7i

A: A complex number 2+5i-4-7i is given. First simplify the complex number by rationalizing it. For…

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: The given complex number is, 1+i12. The objective is to change the given complex number to the form…

Q: Find the standard form of the complex number 6(cos 17°26' + isin 17°26'). Round values to the…

A:

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given: Let z=1-3i3 To Find: To change the given complex number into a+ib form using De Moivre’s…

Q: Find the product of the complex numbers z1 = 4(cos 50° + i sin 50°) and z2 =  7(cos 100° + i sin…

A: Given complex numbers - z1 = 4cos50°+isin50°                ..........................(1)z2 =…

Q: Express the following complex number in its polar form. 2+5i -4-7i .i'(V3 – i10)(2 – i5)

A:

Q: Solve the following complex numbers: Z1 = 5+3i; Z2 = 4+5i ; Z3 = 3-i 1. The product of Z1*Z2 2. The…

A:

Q: Express the following complex numbers in polar form a: 3+4j b: -3-4j c: 3-4j

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

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: and of b is Writing the complex number z=2 e6 in the form a+ ib, the value of a is

A:

Q: Express the given complex number in rectangular form (a + ib). T 1. + i sin + i sin cos 9. 9.

A:

Q: Write the following complex numbers in rectangular form (z = x + iy) el-i +1 el-i – 1'

A: I have divide each terms as a+ib form the rationalized

Q: Express the complex number 10(cos a + i sin a) in rectangular form Z = a + bi. Select the correct…

A: For the following complex number,

Q: 2. Write the complex number 3+5i 5-3i in the form a + bi.

A:

Q: Z is a complex number

A:

Q: Express the following complex number in exponential form: (-1 – 5) 3.1 e2.5i 5.1 e4.5i -5.1 e4.5i…

A:

Q: Find the product of the complex numbers z1 = 6(cos 40° + i sin 40°) and z2 = 5(cos 20° + i sin 20°).…

A: Given  z1 =6cos 40° + i sin 40° z2 =5cos 20° + i sin 20°

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: Find the magnitude of the resulting complex number, 6 (cos 120° +i sin 120°) x 4 (cos 30° + i sin…

A:

Q: Find the four fourth roots for the complex number: v2 + v2i

A:

Q: logz, (z3":) \0gz;

A:

Q: 2. Write the complex number 3 + 5i 5 - 3i in the form a + bi.

A:

Q: Represent the following complex numbers in polar form: 6. -i 7. -4 8. 2+2/3i 9. -5+ 5i 10. 2 – 2i…

A: 6. It is given that the complex number -i, Note that: The complex number a+ib  can be written in…

Q: Express the following complex number in polar form. i. -3 - j4

A: Given that z= -3-4j , z=x+iy is cartesian form  then polar form is z=r(cosθ+isinθ) , where  z=x2+y2…

Q: Express the following complex numbers in polar form: (3+ /3i) (-1-i)² 2 i) z=(3 -i) ii) iii) 1-iV3

A:

Q: 2. What is the standard form of the complex number –13.5(cos() + i sin())?

A:

Q: z = sin(e³) + sinh(5230°)

A:

Q: Express the following complex numbers in standard form a ± bi. 12 +V-81 (a) (b) (2— 6і) (3 +)

A:

Q: Find the quotient z1/z2 of the complex numbers. Leave the answer in polar form with the argument…

A:

Q: Divide the complex numbers below and leave t trigonometric form. 7(cos 150° + i sin 150°) 9(cos 190°…

A: