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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
- If z=(1+7i)/((2-i)^2) , then (a)|z|=2 (b) |z|=1/2 c) a m p(z)=pi/4 (d)...
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- The value of (i^5+i^6+i^7+i^8+i^9)/(1+i) is (a) 1/2(1+i) (b) 1/2(1-...
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- Write the least positive integral value of n for which ((1+i)/(1-i))^n...
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- If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (a)(|z|)/2 ...
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- If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...
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- What is the locus of z , if amplitude of (z-2-3i) is pi/4?
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- Write the sum of the series i+i^2+i^3+....... upto 1000 terms.
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- The sum and product of two complex numbers are real if and only if the...
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- If ((a+i)^2)/((2a-i))=p+i q , show that: p^2+q^2=((a^2+1)^2)/((4a^2+1)...
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- Write the value of a r g(z)+a r g(barz ) .
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- Find the conjugate of (1-i)/(1+i)
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- Find the conjugate of 1/(3+4i)dot
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- If (a+i b)/(c+i d)=x+i y , prove that (a-i b)/(c-i d)=x-i ya n d(a^2+b...
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- Find real values of xa n dy for which the complex numbers -3+i x^2ya n...
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- Find the real values of x and y for which (1+i)y^2+(6+i)=(2+i)x
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- Find the real values of xa n dy , if (3x-7)+2i y=-5y+(5+x)i
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- If (x+i y)^(1//3)=a+i b ,x ,y ,a b in Rdot Show that x/a+y/b=4(a^2-b^...
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- If a+i b=(c+i)/(c-i) , where c is real, then :a^2+b^2
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- Evaluate the following: i^(135)
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- Evaluate the following: i^(19)
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