Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Recall that the symbol z represents the complex conjugate of z. If z = a + bi and w = c + di, prove the statement.z2  = z2 Working from the left-hand side, simplify the expression into the standard complex form.

Recall That The Symbol Z Represents The Complex Conjugate Of Z If Z A Bi And W C Di Prove The Statementz2 Z2 Working From The Lefthand Side Simplify The Express class=

Sagot :

taeuknam

Hi elsmith,

w is the complex conjugate of z (and vice versa), and we are asked to prove that w^2 is equal to the complex conjugate of z^2.

If z = a + bi and w = c + di, the complex conjugate of z is a - bi (that's what complex conjugate is, same real part, the negative of the imaginary part).

Then c = a and d = -b. w = a + -bi.

Square z. cc(z) I define to mean the complex conjugate of z. cc(z^2) = cc(a + bi)^2

= cc(a + bi)(a + bi) Now, use FOIL.

= cc(a^2 + abi + abi + (b^2)(i^2)) I squared is -1, so the last term is the same as -b^2.

= cc(a^2 - b^2 + 2abi)

= a^2 - b^2 - 2abi

Now, square w. w^2 = (a + -bi)^2

= (a + -bi)(a + -bi)

= a^2 - abi - abi + ((-b)^2)(i^2)

= a^2 - b^2 - 2abi.

So, z^2 and w^2 are indeed equal, proving the claim.

If you have any further questions, feel free to message me!

Sincerely, taeuknam.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.