Complex number
1) Simplify: 1+ i² + i⁴+ i⁶.
2) Show that: [i³⁷ - (1/i)⁴¹]³= 8i.
3) Find the conjugate of (2+ 3i)².
4) Find x and y if (3x -7)+ 5iy = 2y +3 -4(1- x)i.
5) Find the modulus of -12+ 5i.
6) Express the reciprocal of the complex number 3+ i √5 in the form of a+ ib.
7) Find the modulus of (1+ i)/1- i)/(1- i)/(1+ i).
8) Find the solution of the equation |1- i|ˣ= 2ˣ.
9) Show that the points representing the complex numbers (3+ 3i), (-3-3i) and (-3√3+ 3√3 i) are the vertices of an equilateral triangle.
10) Express (3+ i)/(-5- 4i) in the standard form a+ ib.
11) Find the modulus of (2+ 3i)/(3+ 2i).
12) Prove that the representative points of the complex numbers 1+ 4i, 2+ 7i, 3+ 10i are collinear.
13) Find the modulus of
{(3+2i)+1+ i)(2+ 3i)}/{(3+ 4i)(4+ 5i)}.
14) If x+ iy = √{(a+ ib)/(c + id)}, show that (x²+ y²)²= (a²+ b²)/(c²+ d²).
1) 0 3) -5-12i 4) 6,4 5) 13 6) 3/14 - √5i/14 7) 2 8) 0 10) -19/41 +7i/41 11) 1 13) 13√2/5√41
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