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The Complex Number 3 3i 1 I 3 3i I 3 3i When Represented In The Argand Diagram

Solution: Given z = (-√3+3i)(1-i)/(3+√3i)(i)(√3+√3i) Taking √3 outside =... View Article

If 5z2 11z1 Is Purely Imaginary Then The Value Of 2z1 3z2 2z1 3z2 Is

Solution: Given 5z2/11z1 is purely imaginary Let us take 5z2/11z1 = iy z2/z1 = 11iy/5 |(2z1+3z2)/(2z1-3z2) = z1(2+3z2/z1)/z1(2-3z2/z1) =... View Article

The Conjugate Of The Complex Number 1 I 2 1 I Is

Solution: (1+i)2/(1-i) = (1+i)2(1+i)/(1-i)(1+i) = (1+2i-1)(1+i)/(1--1) = 2i(1+i)/2 = (2i-2)/2 = (-1+i) Conjugate is -1-i. Hence option (4)... View Article

The Amplitude Of Sin Pi 5 I 1 Cos Pi 5 Is

The amplitude of sin π/5 + i (1-cos π/5) is (1) 2π/5 (2) π/15 (3) π/10 (4) π/5 Solution: Given sin (π/5)+i(1-cos (π/5) =... View Article

If X Iy Aib C+Id Then X 2 Y 2 Is Equal To

Solution: Given x+iy = √((a+ib)/(c+id))...(1) Taking conjugate on both sides x-iy = √((a-ib)/(c-id)) ..(2) Multiply (1) and (2)... View Article

The Modulus Of 1 I 3 I 4i 5 Is

Solution: (1-i)/(3+i) +(4i/5) = (5-5i+12i-4)/(3+i)5 = (1+7i)/(3+i)5 Multiply numerator and denominator with (3-i) = (1+7i)(3-i)/(3+i)5(3-i)... View Article

The Solution Of Equation Z Z Equal 1 Plus 2i Is

Solution: Given |Z| - Z = 1 + 2i |Z| = Z +1 + 2i Take Z = x+iy |Z| = √(x2+y2) Z +1 + 2i = x+iy+1 + 2i = (x+1)+i(y+2) since |Z|... View Article

For Any Complex Number Z The Minimum Value Of Z Plus Z 1 Is

Solution: |Z| + |Z - 1| = |Z| + |-(1-Z )| = |Z| + |1-Z | (since |Z| = |-Z| |Z| + |1-Z | ≥ |Z+1-Z| |Z| + |1-Z | ≥ 1 |Z| + |-(Z-1) |... View Article

If Z 4 By Z Equal 2 Then The Maximum Value Of Z Is

Solution: For any two complex numbers a and b ||a|| ≤|a-b| ||z| -|4/|z| |≤ | z-4/z| => |z| -4/|z| ≤ 2 Set |z| = r > 0,... View Article

Let Z And Omega Be Two Non Zero Complex Numbers Such That Z Equal And Arg Z Arg Omega Equal Pi Then Z Equals

Let z and ω be two non zero complex numbers such that |z| = |ω| and Arg z +Arg ω = π, then z equals (1) ω (2) -ω... View Article

If Z1 Equal Root 2 Cos Pi By 4 I Sin Pi By 4 Z2 Equal Root 3cos Pi By 3 Plus I Sin Pi By 3 Then Z1z2 Is Equal To

Solution: Given z1 = √2(cos π/4 + i sin π/4) z2 = √3(cos π/3 + i sin π/3) |z1| = √[(√2 cos... View Article

If The Conjugate Of X Plus Iy 1 2i Is 1 I Then

Solution: Given conjugate of (x + iy)(1-2i) is 1 + i. Conjugate of (x + iy)(1-2i) => (x-iy)(1+2i) = 1+i (x-iy) = (1+i)/(1+2i) Multiply... View Article

If Z1 And Z2 Are Two Complex Numbers Such That Z1 Equal Z2 Plus Z1 Z2 Then

Solution: Given |z1| = |z2| + |z1 - z2| |z1| - |z2| = |z1 - z2| Squaring both sides (|z1| - |z2|)2= |z1 - z2|2 |z1|2 +|z2|2-2|z1 ||z2| =... View Article

Convert I 1 Cos Pi 4 I Sin Pi 4 In Polar Form

Convert (i+1)/(cos (π/4)-i sin (π/4) in polar form (1) cos (π/4)+i sin (π/4) (2) cos (π/2)-i sin (π/2)) (3) √2(cos... View Article

If Z Is A Complex Number Such That Re Z Im Z Then

Solution: Let z = x+iy Given Re(z) = Im (z) => x = y z2 = (x+iy)2 = x2+2ixy-y2 = 2ix2 (since x = y) Re (z2) = 0 Im (z2) = 2ix2 Hence... View Article

If 1 I 2 2 I X Iy Then X Y Is Equal To

Solution: Given (1+i)2/(2-i) = x+iy (1+i)2/(2-i) = (1+i)2(2+i)/(2-i)(2+i) = (1+2i-1)(2+i)/(4--1) = 2i(2+i)/5 =( 4i-2)/5 = (-2+4i)/5 x =... View Article

If Z X Iy And Z 1 3 P Iq Then X P Y Q P 2 Q 2 Is Equal To

Solution: z = x-iy z1/3 = p + iq x-iy = (p3-3pq2)+i(3p2q-q3) Comparing we get x = p3-3pq2 and y = -3p2q+q3 (x/p)+(y/q) = p2-3q2-3p2+q2 =... View Article

What Is The Product Of A Number

In Mathematics, the term “product” is the result of the multiplication operation. If the given numbers are multiplied together, we get the result... View Article

How Do You Multiply Real And Imaginary Numbers

We know that a complex number is a combination of real numbers and imaginary numbers. The complex number may be either real or imaginary if one... View Article

What Is Mean Deviation And Standard Deviation

Mean Deviation: Mean Deviation means how far the values are from the middle of the data set. The procedure to calculate the mean deviation is as... View Article

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