Express the complex number z = :-1+i/3 in the form z = re and then find z.

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: Express the complex number z =1- 3i in the form of ree and deduce the following complex numbers in…

A:

Q: Write the complex number in polar form with argument 0 between 0 and 2r. 5 + 5/3i () 101 cos + i sin…

A:

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: 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+i8  To Find: To change the given complex number into a+ib form using De Moivre’s…

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: 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: Find the radius  and angle of each complex number.  Z=4-3i Z=2+3i Z=3 Z=1+i Z=8+i

A:

Q: Rewrite the complex number 9e2.54 in a + bi form

A:

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

A: See the details solution below

Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: -1 - sqrt(3)/3 i = -1 - 0.577i (approx) This is similar as (-1,-0.577). Plotted it on graph.

Q: z =1+2i

A:

Q: Express the given complex number in polar and rectangular forms. 10.0 e 1.20j

A: We have to write polar and rectangular form of given complex number:

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

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: Graph the complex number, find its modulus and put the complex number in polar form with argument θ…

A: First, we will graph the given complex numbers.(a) 7−3i(b) −1−√33i(c) −√2+i√22(d) −5 + 5√3i

Q: Transform the complex number into its rectangular (1+5i)

A: (1+5i)

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

A: Consider the given: z=3It can be written as:z=3+0iComparing z=x+iy,here,x=3,y=0

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

A:

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

A:

Q: Plot the complex number z = 2 + 5i and find its absolute value.

A: Given:z=2+5i

Q: Find the following products of complex numbers a. (2 + 3i)(4 - 2i) b. (-1 - 2i)(2 + i)

A:

Q: Find the principal root of the complex number: (1– (2+ 4i)²

A:

Q: (3+ /3i) (-1-i)?

A:

Q: Given the complex number z such that z-4i = a+3zi , find the value of a if z is purely imaginary.

A:

Q: Rewrite the complex number 8e.b in a + bi form. Round to two decimal places.

A: The given complex number 8e1.5 i

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: Find the product of the complex number z = 3 + 4i and its conjugate z*.

A: The complex number is given as z=3+4i

Q: Find the product of the complex numbers z1 = 1 + i and z2 = 2 + 2i. Leave answers in polar form.

A: First multiply the given complex numbers. z1·z2=1+i2+2i=2+2i+2i-2=4i Obtain r. r=42r=4

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: Write the complex number in polar form with argument 0 between 0 and 2m. -VZ+ V6i

A:

Q: Find all complex numbers z E C that satisfy the equation (7) + 3 = 0.

A: Solve the following

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

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

Q: Plot the complex number on the complex plane and write it in polar form and in exponential form.…

A:

Q: Z = (1 - j)¹-2j

A:

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: Find the roots of complex numbers. z5 = 4i

A:

Q: Express the given complex number in polar form z=-5*square root of 3 - 5i)

A:

Q: Find the real and imaginary parts of the complex number.

A: Concept  -If a complex number is given as - z = a+biThen,a = real partb = imaginary part

Q: Write the complex number in polar form with argument e between 0 and 2N. 6 + 6V3i

A: We have to find the polar form