For example, √-36 = √(36 × -1) = √36 ×√-1 = 6i In general, for any positive real number a, √(-a) = (√a) i What is the difference between a complex number and an imaginary number?Consider again the complex number a + bi. If a is not equal to 0 and b = 0,...
Prove that, if z is a complex number, then e^z+e^z and e^z* e^z are both real. What can you say about e^z-e^z and e^z÷ e^z?相关知识点: 试题来源: 解析 e^z-e^z is imaginary, e^z÷ e^z has modulus 1.反馈 收藏 ...
Complex numbersexponentsnumber systemsMost any students can explain the meaning of a b , for a ∈ R and for b ∈ Z . And some students may be able to explain the meaning of ( a + b i ) c , for a , b ∈ R and for c ∈ Z . However, few may be able to explain a d i ...
How many real number solutions are there to the equation 0 = -3 x^2 + x - 4? How many real number solutions does the equation have? y = -5 x^2 + 8 x - 7. What is a non-real, complex number? To what subset of the real number system does the number -0.75 belong and ...
If z is a complex number satisfying ∣∣z2+1∣∣=4|z|, then the minimum value of |z| is A2√5+4 B2√5−4 C√5−2 Dnone of theseSubmit If z a complex number satisfying ∣∣z3+z−3∣∣≤2, then the maximum possible value of ∣∣z+z−1∣∣ is - A2 B3√2 C2√...
The principal value of a complex number {eq}z {/eq} is the value for {eq}\theta {/eq} that occurs within a predefined range of values, usually, but not always, {eq}(-\pi,\pi] {/eq}. The idea of the principal value is extended to areas in complex analysis where similar ...
Before moving to arithmetic operations on complex numbers, observe one more important relation between the cartesian and polar form of a complex number. You have seen how to write the polar form from the cartesian form. How do we do the reverse? This is quite straight forward: ...
For example: (where p and q are polynomials). Some fields simply can’t be approached without complex numbers, particularly quantum mechanics. In QM the probability of something happening is the square of the magnitude (absolute value) of the “probability amplitude”, which is complex-valued. ...
If z=x+, the conjugate complex number x- is conventionally represented by z. What is the geometrical representation of z?相关知识点: 试题来源: 解析 With reference to Figure we see that z is represented by the reflection of the point representing z in the real axis....
What Is an Economy? An economy is a complex system of interrelated production, consumption, and exchange activities, which ultimately determine how resources are allocated among participants. The production, consumption, and distribution of goods and services combine to fulfill the needs of those living...