SOLUTION: Let z = a + bi represent a general complex number. As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a + bi) is the complex number a-bi. Also, the modulus of

Question 319283: Let z = a + bi represent a general complex number. As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a + bi) is the complex number a-bi. Also, the modulus of z, modulus(z) is the "size" of z, or SQRT(a2 + b2). Which of the following is true for all complex numbers?
I am having a really hard time with this problem. Help would be greatly appreciated.
Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let z = a + bi represent a general complex number.
As noted in the lesson, the conjugate of z, abbreviated conj(z) or conj(a + bi) is the complex number a-bi.
Also, the modulus of z, modulus(z) is the "size" of z, or SQRT(a2 + b2). Which of the following is true for all complex numbers?
-----------------------
A All of the following
False because E is not true
---------------------------------
B z*conj(z) = [modulus(z)]^2
---
true because (a+bi)(a-bi) = a^2+b^2 which is the square of the modulus
------------------------
C z + conj(z) = 2a
---
true because a+bi + a-bi = 2a
--------------------------------
D z - conj(z) = 2bi
true because a+bi -(a-bi) = a+bi-a+bi = 2bi
--------------------------------
E None of the above
False because b, c, and d are all true
=======================
Cheers,
Stan H.
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