Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.