Porisma

A hint to get started

Complex roots without a graphing calculator

A graphic calculator is not to be used in answering this question.

Solve the equation z2=3−4iz^2=3-4i, giving your answers in the form a+iba+ib. Hence, by expressing 13i−14\frac13i-\frac14 in the form k(3−4i)k(3-4i), where kk is a constant, find the roots of the equation

w2=13i−14w^2=\frac13i-\frac14.

CJC · Discussion · Question 1

Write z as a+ib and compare real and imaginary parts. Then reuse the square root rather than solving a new system.

Read the worked solution