To find the argument of the complex number (1+i)4, we can follow these steps: Step 1: Express the complex number in polar formThe complex number 1+i can be expressed in polar form. We first find the modulus r and the argument θ. The modulus r is given by:r=|1+i|=√12+12=...
The correct Answer is:C To find the argument of the complex number z=(1+i√3)24i(1−i√3), we will follow these steps: Step 1: Expand the numeratorWe start with the numerator (1+i√3)2. Using the formula (a+b)2=a2+2ab+b2:(1+i√3)2=12+2(1)(i√3)+(i√3)2Calcula...
Link to this page:<a href="https://www.thefreedictionary.com/Argument+of+a+complex+number">complex number</a> Facebook Twitter Complete English Grammar Rules is now available in paperback and eBook formats. Make it yours today! Advertisement. Bad banner? Pleaselet us knowRemove Ads...
we have6-a+b=0 and -20+a=0a= 20 and b= 14OR: Since-1+i is a root of 3z³+13z²+az+b=0, then-1- i is also a root the Conjugate Root Theorem.Let 3z³+ 13z²+az+b=(z+1-i)(z+1+i)(3z+A)=(z²+2z+2)(3z +A)By comparing coefficients of z,...
How do you find a complex number given the modulus and argument? What is the complex conjugate of the complex number 2 - 4i? Prove that if z is a complex number then \frac{1}{z}=\frac{\overline{z{|z|^2} . What is the purpose of complex numbers?
4 (a) The complex number z is given by z= re i0, w hercr0andO≤0≤1/2π .(i) Given that w = (√3 -i) z, find |w| in terms o f r and arg w in terms o f 8.[2](ii) For a fixed value o f r, draw on the same Argand diagram the the locus o f z an...
The argument of the complex number (1+i)4 is A135∘ B180∘ C90∘ D45∘Submit What is the arugument of the complex number (1+i)(2+i)3−i where =√−1 ? A0 Bπ4 C−π4 Dπ2Submit What is the argument of the complex number (1+i)(2+i)3−i, where i=√...
NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year pap...
+418The complex number w is defined yw=(22+4i)/((2-i)^2) (i) Without using a calculator, show that w = 2 + 4i.[3](ii) It is given that p is a real number such that 1/4π≤arg(w+p)≤3/4π . Find the set of possible values of p.[3](iii) The complex conju...
After that, the values of the argument {eq}\theta {/eq} and magnitude r of polar coordinates are obtained by the most general relation shown below: {eq}c+id = r(\cos \theta+\sin \theta )\\ y=\sqrt{c^2+d^2}\\ \displaystyle ...