Express in exponential form: –8 + 8i/3. 31 Represent graphically the set of values of z for which < 2 2+3 Describe all complex numbers z such that

Q: Consider the complex number 2 + i. Working in exponential form, investigate the effect of…

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-2 - 7i

A: z=-2-7i Now, r=-22+-72=53 &amp; θ=tan-1yx=tan-1-7-2=π+tan-172      ∵The given complex number lies in…

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: Find the 5™ roots of the complex number [(2+x) – 5i] , where x = last digit of your ID Number.

A: To find- Find the 5th roots of the complex number 2 + x - 5i, where x = 2

Q: Find (5i – 5)/(1 – 2i) in real-imaginary form.

A: The complex numbers are imaginary numbers. They are not considered a real number. The imaginary…

Q: Represent the complex number geometrically.(1 + 2i)2

A: Represent the complex number geometrically.(1 + 2i)2

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 2n. 7 - 7i

A: The expression of the polar form is given by z=rcosθ+isinθ Given complex number is (x+iy)=7-7i. The…

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

A:

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

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

Q: Use DeMoivre's Theorem to raise the complex number to the given power. Express your solution in…

A: Compare the given complex number with the standard form and find x and y.Find theta using x and y.

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-10 + 10i

A: We have given  z = -10 + 10i    Now, z can written as reiθ    r =  (-10)2+ 102              [ As if…

Q: Let z be a complex number with |z = 11 and let z0 = 17 – 20i. What is |z – z0| + |z+ zo|??

A: Given:- Let z be complex number with |z| =11 and z0 =17 -20i  To find:- value of |z - z0 |2 +  |z…

Q: Find two complex numbers a + bi in which a 0 V17 and b 0 with a modulus of

A: topic - complex numbers

Q: Use DeMoivre’s theorem to find (–8)1/3. Express your answer in complex form.

A:

Q: Show that -1+ /3i is a cube root of 1 (meaning that its cube equals 1).

A: Find the cube of the expression and prove that it is equal to 1

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 z = 10 cis 315° in rectangular form a + bi.

A: Given the complex numberz=10cis315°

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-17

A: Let z=−17⇒z=−17+i0The complex form z=x+iy in trigonometric form is written asz=rcosθ+isinθ,…

Q: Find all complex square roots of -4i. In other words, find all complex solutions of x =-4i. i

A: Find the all complex solutions

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

A: Given :            -22 + 22i15   To change the given complex number to the form a + bi using De…

Q: Find all complex numbers satisfying |z + 3 + 4i| = |z − 5|

A: Topic:- complex numbers

Q: (1–/3i)2015 4028 [V2cis(쯤)] = Z

A:

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. -z

A:

Q: Solve the following  complex numbers in their rectangular form.  Where in Z1=2+4i, Z2 = 5e2i and Z3…

A:

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: V3 1 (- 2

A: given(-32-12i)20 =(-1)20(32+12i)20 =(cos30+isin30)20 The formula of Demoivre's theorem is cos θ+isin…

Q: Express the following complex number in exponential form: (3 - 4) O -V5e-5.36/ 5e5.361 5e-5.36i…

A:

Q: Write complex number in standard form Z=3(cos240+i sin240)

A: To write given complex number in standard form, substitute the value of  and:

Q: Use de Moivre's formula to evaluate (-2 + 2i)1º. Express your answer in standard form or, in a + bi…

A: De Moivre's Formula: For any positive integer n and complex number x=a+ib, the de Moivre's formula…

Q: Write the complex number z=(1-√3i)2015/(√2cis(7π/6))4028 in an exponential form.

A: cis(x) = cos(x)+isin(x)

Q: Present complex number z in algebraic form =* + 23D 35 1-3i

A:

Q: Express in the form , where a and b are a+bi real numbers.

A: To express the given expression in the form of (a+bi),where,(a,b∈R). (4+2i)(-5+4i) Solution:…

Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form

Q: complex numbers.

A:

Q: Express the complex number z = 10 cis 270° in rectangular form a + bi.

A:

Q: Express in the form , where a and b are a+bi real numbers.

A: We have to express the express in a+bi form for the given expression: 3+8i2 We know that…

Q: Find all complex square roots of -2+2/3i. In other words, find all complex solutions of x=- 00..

A:

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

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.-6i

A: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.z=-6i=0-6i

Q: Ifz is a complex number, then sin-z can be written as (A)-i In iz+ (1-z) (B)t In [iz + (1 -z)]…

A:

Q: give 2 examples of questions and answers for each material namely a. basic functions of complex…

A: Hi there! You seem to have uploaded many sub-parts. As per our norm we will be answering only first…

Q: a) Express the complex number Z 10 (cos 150° +i sin 150° ) in rectangular and exponential form. V3…

A: (a)z=10(cos 150°+i sin 150)where r=10and θ=150*π180=56πExponential form is z=reiθz=10ei5π/6In…

Q: Express in the form , where a and b are a+bi real numbers.

A: Let the given expression be z - z = 7+5i--8+3iz = 7+5i+8-3iz = 7+8+5i-3iz = 15+2i

Q: Prove that x^2 = 4 will result into ± 2 using complex numbers.

A: Given that, x2=4

Q: Let z2 = -V2 + i/3, w = -3+ 3i and p= -3– 2i. 1. Find all the complex numbers given by In z2.

A: It is given that

Q: Exer. 21–46: Express the complex number in trigonometric form with 0 so<27. 25 2V3 + 2i 4 cis 37 29…

A: Given: The complex number 25) 23+2i. 29) -20i 34) -5.