What is the value of \(\sqrt{12+5 i}+\sqrt{12-5 i}\) where \(i=\sqrt{-1}\) ?
5√2
The principal roots are \(\sqrt{12+5i}=(5+i)/\sqrt2\) and \(\sqrt{12-5i}=(5-i)/\sqrt2\). Adding gives \(10/\sqrt2=5\sqrt2\).
Similar Questions
What is the modulus of z?
What is angle θ such that z is purely real ?
where n is an integer
What is angle θ such that z is purely imaginary ?
where n is an integer
If z z̅ = |z + z̅ |, where z = x + iy, i = \(\sqrt{-1}\), then the locus of z is a pair of:
What is the modulus of the complex number \(\rm \frac {\cos \theta + i \sin \theta}{\cos \theta - i \sin \theta},\) where \(\rm i = \sqrt {-1}\) ?
What is the argument of the complex number \(\rm \frac {1 - i\sqrt 3}{1 + i \sqrt 3},\) where \(\rm i = \sqrt {-1}\) ?
What is z 1+ z 2+ z 3equal to?
Consider the following statements:
1. z 1 z 2 z 3 is purely imaginary.
2. z 1z 2 + z 2z 3 + z 3z 1 is purely real.
Which of the above statements is/are correct?\(\left| {\frac{{{\rm{z}} - 4}}{{{\rm{z}} - 8}}} \right| = 1\) and \(\left| {\frac{{\rm{z}}}{{{\rm{z}} - 2}}} \right| = \frac{3}{2}\)
What is |z| equal to?
\(\left| {\frac{{{\rm{z}} - 4}}{{{\rm{z}} - 8}}} \right| = 1\) and \(\left| {\frac{{\rm{z}}}{{{\rm{z}} - 2}}} \right| = \frac{3}{2}\)
What is \(\left| {\frac{{{\rm{z}} - 6}}{{{\rm{z}} + 6}}} \right|\) equal to?
Important Questions from Properties of Complex Numbers
The Real part of \(z = \frac{{5 + 2i}}{{2 - 5i}} - \frac{{3 - 4i}}{{4 + 3i}} - \frac{1}{i}\) is
What is the modulus of z?
What is angle θ such that z is purely real ?
where n is an integer
What is angle θ such that z is purely imaginary ?
where n is an integer
The curve represented by z z̅ + (1 + i) z +(1 - i) z̅ = 0 will be:
