(b) Show that i³i is real, even though i or 3i is not.

Q: (b) Show that i10 is real, even though i or 10i is not.

A:

Q: Determine the argument and the modulus of the given complex (-2-4i)(5i) number: (3+8i)

A:

Q: 4. Find the modulus, Iz], and argument, 0 , of the complex number. -1 + i

A:

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: 2. Express the product of (3 - 2i) and (1 + 5i) divided by the product of (5 + 2i) and (-4 - i) in a…

A: Given expression is 3-2i 1+5i5+2i -4-i. Simplify the above expression as follows.

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: Let a = 1+bi be a complex number, b>0, such that a is a real number. Evaluate 1+a+a² + . + a". ....

A: Given a complex number : a=1+bi where b>0 It is given that  a3 is a real number. We need to find…

Q: Find the principle root of 8/. (A) 8i = 3 +1 (C) V8i = 3 + 2/ (B) V8i = 23+1 (D) V8i = 2/3 +8i - %3D…

A:

Q: Find the conjugate of – 3i ( 2 + 5i ).

A: Solution

Q: Find the modulus of the complex number. -5- i

A:

Q: Represent the complex number geometrically.2i(2 + 3i)

A: given 2i(2+3i) =4i-6=-6+4i It is represented in a complex plane. where x-axis represents real value…

Q: (b) Show that i0 is real, even though i or 6i is not.

A:

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

A: We have to express given number 20-8i4i in the form a+bi where a and b are real numbers.

Q: Two complex numbers z1 and z2 are given by z1 = 3 + 2i and z2 = − 1 − 4i. Evaluate, (a) |z1z2| (b)…

A:

Q: Which of the following is the standard form for the product of (2 + 3i)(2 3i)?

A:

Q: Express 3-i/2+3i  in the form a + bi

A: Rationalise i^2=-1

Q: Visualize the addition of (3 + 6i) + ( – 7 – 8i) by plotting the initial point, and the result. 10+…

A:

Q: of the complex number: (27V3 27 3

A:

Q: 2. Write the number (2 – i)(-1+3i)(3 – 4i) in the form of +bi .

A: The detailed solution is as follows below:

Q: Find x and y so that the following -2-7i =x+ yi equation is true:

A: Given -2-7i=x+yi

Q: What is the conjugate of - 3 + 4i?

A: Any number of the form a+ib where a and b are real numbers and i=-1 is called a complex number. The…

Q: The conjugate of -4 -3i is............

A:

Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

A:

Q: Represent the complex number geometrically.4(-1 + 2i)

A: 4-1+2i

Q: Express the complex number in exponential form. z=4-6i

A:

Q: Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A: Given:        z=−4+3i,  zw=−7−2i

Q: (b) Show that it is real, even though i or 8i is not.

A:

Q: Let z = -4 + 3i and zw = -7- 2i. By showing clear steps, find w in the form of a+bi.

A: Given  z=−4+3izw=−7−2i

Q: 5) A = 2i+3j+5k and B = 3i+6k, Determine the direct cosine of (AXB). %3D %3D

A: Finding the cross product of vector A and vector B  i×i=j×j=k×k=0, i×j=k, j×k=i, k×i=j, j×i=-k,…

Q: . Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A: In this question , the value of z is inserted into zw=-7-2i, and then it is solved for value of w.

Q: 4. Find x and y so that the 1ollowing equation -2-7i =x+ yi is true:

A:

Q: If |x = 3i| <5, then prove that the complex number z also satisfies the inequality i(z+1)+1| <25.

A:

Q: Find the quotient of (2√3+2i)(-4+i) 2 (1-√3i)

A: Solution

Q: Visualize the multiplication of (2 + i)( – 2 – 3i) by plotting the initial point, and the result.…

A: Given,           2+i-2-3i

Q: 6- The Conjugate of 4+3i =-(4+3i)

A: The objective is to find the conjugate of (4+3i).

Q: (a) Simplify i*+1 in real and imaginary parts.

A: As there are two questions given ,i only do the first.

Q: Represent the complex number geometrically.3 - 5i

A: The complex number 3-5i

Q: The conjugate of 2 - 9i is________.

A: Given complex number z - z = 2-9i                       ....................(1)Concept - If a…

Q: Find the distance d between 21 1 = (-7- 6i) and %3D z2 = (-15 – 12i). %3D

A: z1=-7-6iz2=-15-12i We can say that the co-ordinates of two points are (-7,-6) &amp; (-15,-12).…

Q: Express (5 – 3i)3 in the form a + ib.

A:

Q: ;5i (b) Show that ¿" is real, even though i or 5i is not.

A: We have i5i Now, we can write ab=elnab Also, lnab=blna , therefore: ab=elnab=eb lna So, using ab=eb…

Q: 7. Plot the complex number 3 - 6i

A:

Q: (b) Show that ii is real, even though i or 5i is not.

A:

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: (5) Yz-3-4i, what is in standard form a+ ib?

A:

Q: find w., of ((1+ 2i) + (3 – 4i)) 7

A: Given that, 1+2i+3-4i12