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What is the complex number of z 2 - Ii?
The complex number of the equation z = x + iy is x.
What is the usefulness of the conjugate and its effect on other complex numbers?
The conjugate of a complex number is the same number (but the imaginary part has opposite sign). e.g.: A=[5i - 2] --> A*=[-5i - 2] Graphically, as you change the sign, you also change the direction of that vector. The conjugate it's used to solve operations with complex numbers. When a complex number is multiplied by its conjugate, the product is a real number. e.g.: 5/(2-i) --> then you multiply and divide by the complex conjugate (2+i) and get the following: 5(2+i)/(2-i)(2+i)=(10+5i)/5=2+i
What is the product of the complex number a plus bi and its conjugate?
The product is a^2 + b^2.
How do you divide complex numbers?
When dividing complex numbers you must:Write the problem in fractional formRationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.You must remember that a complex number times its conjugate will give a real number.a complex number 2+2i. the conjugate to this is 2-i1. Multiply both together gives a real number.(2+2i)(2-2i) = 4 -4i + 4i + (-4i2) (and as i2 = -1) = 8To divide a complex number by a real number simply divide the real parts by the divisor.(8+4i)/2 = (4+2i)To divide a real number by a complex number.1. make a fraction of the expression 8/(2+2i)2. multiply by 1. express 1 as a fraction of the divisor's conjunction. 8/(2+2i)*(2-2i)/(2-2i)3. multiply numerator by numerator and denominator by denominator.(16-16i)/84. and simplify 2-2i
Is The product of a complex number and its conjugate is a real number.?
Yes. This is easy to prove; in the following, I'll use "^" for powers. Let the complex number be (a + bi), then its conjugate, by definition, is (a - bi). Multiplying them, you get a^2 + abi - abi + bi^2 = a^2 + bi^2 = a^2 - b^2 (since i^2 = -1).Update: One interesting, and quite useful, property is that the product of the complex number and its conjugate is equal to the square of the absolute value of the complex number.
