Complex Numbers questions
967 published questions with worked solutions.
- If =- 1 2 +i 3 2 then what is vmatrix 1+ &1+ ^2& + ^2 1& & ^2 1 & 1 ^2 &1 vmatrix equal to?
- What is ( 3 +i 3 -i )^ 3 equal to?
- If x^2-x+1=0, then what is (x- 1x )^2+ (x- 1x )^4+ (x- 1x )^8 equal to?
- If z 0 is a complex number, then what is amp (z)+ amp ( z) equal to?
- If = -1+ -3 2 then what is the value of (1+ ^ 19 - ^ 35 )^ 100 -(1-3 ^ 25 + ^ 38 )^ 50 ?
- Let 1, , ^2 be three cube roots of unity. If x=a+b, y=a +b ^2, z=a ^2+b , then what is x^2+y^2+z^2 equal to?
- Let Z_1 and Z_2 be complex numbers such that 3Z_1 4Z_2 is purely imaginary. What is | Z_1+Z_2 Z_1-Z_2 | equal to?
- If , , are cube roots of -8, then what is ^2p^2+ ^2q^2+ ^2r^2 ^2p^2+ ^2q^2+ ^2r^2 equal to?
- If p, q, r are the cube roots of unity, then what is vmatrix p^2+q^2&r^2&r^2 ^2&q^2+r^2&p^2 ^2&q^2&r^2+p^2 vmatrix equal to?
- If (1+i)^n-16=0, where i= -1 and n is a positive integer, then what is the least value of n?
- What is i i^4 i^9 i^ 16 i^ 576 , where i= -1 , equal to?
- If z=x+iy be such that | z+ i z- i |=1, where i= -1 and is a positive real number, then which of the following statements is/are...
- The smallest positive integer n for which ( 1-i 1+i )^ n^2 =1 where i= -1 , is
- If Z=1+i, where i= -1 , then what is the modulus of Z+ 2 Z ?
- Consider the following in respect of a complex number Z : 1. (Z^ -1 ) =( Z )^ -1 2. ZZ^ -1 =|Z|^2 Which of the above is/are...
- Consider the following statements in respect of an arbitrary complex number Z : 1. The difference of Z and its conjugate is an...
- What is the modulus of the complex number i^ 2n+1 (-i)^ 2n-1 , where n N and i= -1 ?
- If x^2+x+1=0, then what is the value of x^ 199 +x^ 200 +x^ 201 ?
- What is _ n=1 ^ 8n+7 i^n equal to, where i= -1 ?
- If z=x+iy, where i= -1 , then what does the equation z z +|z|^2+4(z+ z )-48=0 represent?
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