3) Find the complex conjugate and the modulus of the number z: a) := 12 – 5i b) 2= -5i c) 2=-1+2/2 i d) z= -V3- 3i e) 2= --i

Q: jet Za = end P- 1ti Express La for m on their exponential

A: A.)Given values are  Z2=3-i3 ,w=1+2i,p=1+i To evaluate Z2w Let  Z=Z2wZ=3-i31+2i Taking log on both…

Q: Prove the Euler's formula: e" = cos0+ jsin 0 using the definition of the complex number

A: We have to prove that ejθ=cosθ+jsinθ. We know that ex=1+x+x22!+x33!+x44!+.......... Now,…

Q: For the complex numbers • w = 3-5 i • z = -4+7 i Enter exact value of the imaginary part of their…

A: Product of two complex numbers (a+ib)(c+id)=ac-bd+i(ad+bc)

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: What is 11/14 divide by 5/6 in simple form

A: First we flip 5/6 and multiply by that.

Q: Simplify, then express each in complex number form “a+bi” 1) -3(4+2i) -2(5-3i) 2) (4+3i)^2 3) 11+2i…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: 1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

A: The given complex number is

Q: (A) Given A = 3i + 5j , B = -4i + j Find the à +B , à – B & Ā. B

A:

Q: Express the product of 9i5(2i³ - 3i16) in a + bi form.

A: 9i15(2i3-3i16) =(9i15)(2i3)-(9i15)(3i16) =18i15+3 -27i(15+16) =18i18 - 27i31 Now i=√(-1) i18=-1…

Q: In(2) The complex number e is equivalent to a) ji b) (1+j} c) 1+ j d) 1- j

A: According to the problem, we have

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 all solutions of the following equationsa a)z/1-z=1-5i   b) (2-i)z+8z^2=0.  c)z^4-16=0

A: a). z1-z = 1 - 5i⇒ z = (1-5i)(1-z)⇒ z = 1 - z - 5i + 5iz⇒ (2 - 5i)z = 1-5i⇒ z = 1-5i2-5i

Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: Q1) Find modZ and ArgZ for the complex numbers given below: 1+i√2 1-i√2 2 2+i a) Z= b) Z= +2-i

A:

Q: If z=3-4i then express these following complex numbers in the form of a+ib: (a) (=+1)(=+i) 2z (b)

A: If z = a + ib and w = c + id then z+w = (a+ib) + (c+id)       = (a+c) + i(b+d)

Q: Express e a) 0-e²i b) 0+e²i c) e² - ei c) e² +e²i in a +ib form.

A:

Q: 1. Solve the following equations. a) (7+2/)+(4-3) b) (5-2/ (2-)(4+2) d) 2- 1+2 e) 21-3 2. Find x in…

A:

Q: Z₁ = (1+i)² 2 (1 - i)² 3 I

A:

Q: a) Let a complex number z =-5i+3. Find in the standard form x+ yi . IN

A:

Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i

A: To simplify the given complex expression:- 5-i3-i

Q: 4. Evaluate these complex numbers: (a) (40/50° + 20/-30°)¹/2

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: Perform the following operations on the complex numbers. a) (4– 6i) – (-8 - 9i) b) (4 – 6i)(-8 – 9i)…

A: (a) Perform the subtraction operation for the given complex numbers.…

Q: The complex numbers z, and z2 are such that z, = -2 + 2i and zz = -2– 2i. Find (a) arg z1 (b) |z21".

A: we have to find the value of the following

Q: 7. Express the complex number 1/(1+ jV3) in the form Aejº

A: