What is the product z1 z2 in polar form? 27 21 = 3/2 cis 3 22 = 7 cis 3 O7V2cis () 21/2 cis (7) O7V2cis () 21/2 cis () O 3/2 cis (T)

Q: 1. (i) Write 3+i in polar form and hence find (3+i) in the form a + ib. You are given =, = (/3 –…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q1) Express in matrix notation: x' = (cos 2t) x y' = x – (sin 2t)y +1 z' = 1- x + 3y

A:

Q: Find the produCtI' 22 n polar form, Wnerezi and 2 are BIVEN below. 21 = 4(cos(61"+i sin(61") 22 = 5…

A: According to Euler's identity, r ( cos x + i sin x) = r eix

Q: 5. Let z1 = a1 + b;i and z2 = az + bzi. (a) Find Im[z,Zz + (Z)? – 2,7 ]. (b) Prove that (z)² = z,² .

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

Q: 6. Show that when 0</z - 11 < 2, Complex Analysis (z-1)" (2-1)(2-3)=-3 (2- #=() 2(z-1)

A: Here we prove this statement by using series expansion.

Q: Ex. (1): the paralel Sum and difference of the given complex numbers. 1. 2. 3. U = 2+3: U = 4+7i…

A: To add complex numbers in rectangular form, add the real components and add the imaginary…

Q: Evaluate the following integral equation as indicated per item. Indicate the identity used for each…

A: Introduction: Differentiation and integration are the two most important operations in Calculus. We…

Q: 12) Based on below complex functions, what is W¹? W₂ 30y - 8 (Cos (4) + + sin (47)) 3 103 = 2 (cos…

A: we have given that  w1=8cos4π3+isin4π3w2=2cos7π3+isin7π3 then what is w1w=?

Q: 2.)S csc-³«(cosa)³da

A: Given ∫csc-3 α (cosα)3dαTo evaluate the integral:

Q: iii) modulus of complex z = e"H equal to а. 3 b.2 С. 1 d. 0

A:

Q: Suppose z=2– 3i, What is a complex function f (z) = – 37 – 2i Re (z) ? —6+ 13і -6- 13i об+13і 6–13i…

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Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz for all complex numbers O if OSArg(z)ST/2 O…

A: We know that  log(z1.z2) =logz1 +logz2 iff -pi&lt;arg(z1) +arg(z2) &lt;pi

Q: 6. Show that when 0 < |-1|< 2, (z-1)(z-3) Complex Analysis (z-1)" 2+2 =-36 z−3) ² A=0 2(z-1)

A: We use substitution and Laurent series expansion.

Q: Q6 : find 1) j(1 – jv3)(v8 +j) 2) (1+j)(1– j/3)² 3) cos-1(2)

A: (1) j(1-j3)(8+j) Use the property (a+b)(c+d)=ac+ad+bc+bd in the expression (1-j3)(8+j) and…

Q: 1- DETERMINE A AND BEC FOR THAT THE FUNCTION: (f:C+a=+b -2 +az +b f(=) = IF = #1-i, 2-1+i (f(1– i)…

A: Continuity of complex function:

Q: a> Lim az + b = 2-2 Complex Constant and sol": Let us a to. Now |az+b (az₁+b) | = |az_azo | = |a1|2…

A: We have to transcribe the following text in digit format.

Q: Express -2+j, 3+ j2, and 1-j2 in polar form and apply DeMoivre's Q6/ (1 – j2) (-2+ j)(3 + j2)…

A: Polar form of a complex number: The polar form of a+jb is rcosθ+jrsinθ, where r=a2+b2 and θ=tan-1ba…

Q: 12. Convert to polar form x² + 4x +y² +4y=0

A: we need to convert into the polar form.

Q: Find the product z₁z2 and the quotient 21. Express your answers in polar form. Z2 Z1 = 4(cos(160°) +…

A:

Q: 2-the polar form of z=(-1-i ) is

A: The given complex number is z=-1-i. Let z=rcosθ+isinθ be its polar form. This implies that,…

Q: . Let complex numbers a and 1/a lies on circles (x – xo)² + (y – yo)² = r² and (x- x)² + (y – yo)² =…

A:

Q: to (1-553)³ (1+5) 8 (-2+52) 4 use De Morvre's theorem Express เก polar form

A: Step 1: first is to divide r1/r2. Step 2: second is to find theta sub 1 minus theta sub 2. Step 3:…

Q: axy' + bxy' +cy = 0 characteristic equation is, ar + (6- a)r +e= 0 case I: two different real roots…

A: We will find out the required solution.

Q: Let z = − √ 3−i. (a) Please find |z|. (b) Please find the argument of z. (c) Please express z in…

A: Given: z=-3-i. To Do: (a) Find z. (b) Find the argument of z. (c) Express z in polar form.

Q: Q10\ Express -2+ j, 3+ j2, and 1- j2 in polar form and apply DeMoivre's (1– j2)' (-2+ j)(3+ j2)*…

A: Cartesian coordinates (x,y) to polar (r,θ) can be converted by, r=x2+y2, θ=tan-1yx Use this formula…

Q: If 2, =1+(2+ 3)i and z, =-2-2i, express z, and z, in polar form. find z,z, in exponential form. (i)…

A: The polar form of the complex number, z=x+iy is represented as z=rcosθ+isinθ. The exponential form…